 
<SS LAUGH> 
S1: they might be so (xx) so anyway, um, finished? the real, item of business for today is uh, for Rob to give his uh, practice for his thesis proposal. this isn't a, um, a straight group meeting either this is uh, uh to be a practice event for uh, for Rob's defense. but what we're_ the protocol of course is that we interrupt Rob on any point on either, content or, uh, presentation-style suggestions, or anything because, um, this this committee definitely will interrupt him, those of you who have been through this know. 
S2: who's on his committee? 
S3: um, oh it isn't up there. um, so Matt of course and Jim Dimmitt, um Steve Baker and Dave Sutep, who's a professor in physics. 
S1: so 
S4: so you have two outside professors? 
S3: mhm 
S1: right. uh although calling Steve, an outsider is [S3: yeah that's true ] so so he's, so it's it's good to know your committee just strategically, for your, defense, um, and, uh, Steve, is gonna be already very familiar with this material and is gonna be pretty familiar with it [S3: mhm ] and uh, uh Dave Sutep is gonna be, uh, completely, comfortable here. 
S3: so f- for those of you who don't know Dave is the director of the program in complex systems, so, that that's how you know it makes sense to have a physics professor, on this, committee. okay, so, um thank you for coming, and i i look forward to your comments however sca- however scathing they may be. um, my talk my, proposal is called a market protocol for decentralized task allocation and scheduling. i would like to start with a concrete example to really motivate the problem, i am addressing here. so, this is a, a stylized um air combat domain. and what we have here is some commander who wants us to perform an air attack. and there are various resources, an- and agents that can help the um commander accomplish this task. um, in this case the commander, simply wants to use a bomber squad and a fighter squad for th- for the air attack, and, um the bomber squad and the fighter squad in turn need, um each need t- to take off from an airfield. um, for this particular problem, there are b- excess resources there are plenty of airfields to satisfy the demand, so we can actually accomplish all the tasks and satisfy this commander without really much difficulty. now the tricky thing comes in if we actually bring in another commander. um this, the second commander, wants you um, perform a ground attack, which involves a bomber squad, a paratrooper squad and a fighter squad and it can be any of these, um squads but it i- he does need all three of those squads. now the problem is these squads in turn need airfields, i- each one needs an airfield, and, but we can't satisfy both of these commanders at the same time, because they need a total of five um squads, but there are only four four units of the airfield available. so, i- if we need to somehow decide what the more valuable task is what the best cost-benefit trade-off is and, alloc- and in this case reallocate the goods, to, um meet the highest value task. uh in this case if we assume the commander, the commander two has a [S2: what's ] higher value we want to reallocate the um, resources in such a way to satisfy him. 
S2: what's the concept of value? 
S3: value i'll i'll get to that le- let's let's just kind of leave that a little bit vague right now we'll we'll just say there there's some, value to, the um, commanders for accomplishing, you know, um tasks, and there may be some costs in providing some of the resources, and i'll i'll formally define what what those, costs and values look like later. 
S1: you know i i think, uh of course the reallocation is interesting but i, wouldn't necessarily, um, trivialize the initial, allocation, in the first place, you might wanna just say, you know how we come up with this original solution, th- in this case, it's easy to find one, but, that's part of, the work is how to, find solutions in these, networks you know the style of your presentation i- it says okay you know where th- i'm really, where i'm really starting is this reallocation problem that's not 
S3: okay w- s- so, so yes, so the the fir- that first resource allocation was part of the, whole allocation problem that wasn't a particularly difficult one, um, it it becomes a really, more challenging problem when you have the limited resources 
S1: right. right so here's for example how (to make it) more difficult. but also in just mentioning the problem, um, you might want to suggest to them that, that the the details of this are really ar- it's just completely contrived, for, a DARPA site visitor <SS LAUGH> and um, uh, and what you're really, after is a general model of uh... you know these kinds of networks. 
S3: okay... so, what we a- what i do then, so i wanna formalize this model, um um, a bit and i do that in a in a task dependence network what i call a task dependence network. that's a very, there's a general model for how, we can do these um, these task allocation problems when we have these sort of hierarchical dependencies and we have to form a supply chain. um, so let me explain the portions of the task dependence network. now these circles throughout the network represent the tasks or the resources. um, in in either case i i actually treat them i- in exactly the same fashion i assume that a task, is performed by one agent on behalf of another, and that the results can't be, replicated for, can't be directly replicated for other agents y- if you want to have if you wanna have this task performed for say, (you know) an- any this task performed for two agents you would hafta have two agents performing it. so in that sense, the tasks are really the same as any resource any discrete resource these are, all discrete so, i um, basically call them goods. so all these circles represent goods which can be either, you know, a task or a resource. um, on this end, i have these box 
S2: so uh you might another way uh another way to rephrase that might be, that, tasks are, resources that are supplied by other, agents, and uh, ma- might need another word but, tasks are, resources that are supplied by other agents and then there's, some, base resources that are supplied in the environment. 
S3: you- that that isn't e- even necessarily quite, the correct characterization you_ the- some of these prod- s- well i'll ge- some some agents 
S1: there sometimes there really is no definition of task as opposed to resources 
S3: th- th- that's the whole point 
S2: (right) 
S1: it's just that sometimes we think of them as tasks and [S3: i- ] sometimes we think of them, [S3: i- it's ] as resources but there's no, distinction 
S3: it may be more natural in some problems or another to call it task or resource, when you're actually characterizing a specific problem 
S1: and some things they might actually really be production chains when (i they) should be things that really are, thought of as resources. 
S3: you know uh, a supply chain you know producing automobiles or a job shop the intermediate um, goods may be, physical resources, that [S1: yeah ] are produced. so, on this end, the boxes are, consumers. and a consumer simply wants to, um acquire some good, some some good, and get some value from doing so. um, on the other hand, on the other end of the supply chain we have suppliers. and these suppliers, are able to supply, a um, a good, um and perhaps at some cost. the interesting agents in the system are really these ones in the middle. all these boxes in the middle are what i call producers. and a producer, um, has some set of inputs and a single output so it it require- it must, um acquire all of its inputs in order to produce its output. it cannot, um do anything with a, with only a subset of its um inputs. so in this case we say that, the if, that the inputs are complementary, whe- when you have to r- acquire all of them to produce. um, for the pre- first example, um this is a solution allocation for the problem and what a solution is, is, okay fir- first let me, back up and say what an allocation is an allocation is just a subset of the of the task dependence network, that indicates which agents bought and sold which goods. um, (and) in this case um, the um the green circles are the goods that are bought or sol- that are bought and sold, and the green agents are the agents that bought or sold something and the and the dark arro- actually i didn't explain what these arcs are, um in the previous thing, the, um the arcs, let me go back, in in_ the arcs indicate input-output relationships, so if an arc from an agent to a good indicates that the agent can, um pr- s- supply that good in some sense, and an arc from a good to an agent indicates that the agent ca- wants to acquire um one unit of that good, as input, or for consumption. so going back to the s- to an allocation, a dark arrow indicates that the agent, um either bought or sold the good and the grey arrows are um, are failed attempts to acquire or sell goods. 
S2: you said this was the first example? 
S3: yes. this_ s- so [S2: th- this ] basically i don't [S2: this ] have this commander two here. 
S2: oh. but you have, the ground attack, there. 
S3: well, we could say that this, this agent exists here but is is not accomplishing anything. 
S2: it might be more clear to people, if you don't have that ground attack (thing there) if you claim this as the first example 
S1: but actually in a way it might be clearer if you do, because, [S2: well but thi- but it looks like ] it shows that that's the way you can ha- that you can accommodate having these, things that are just not useful, [S3: right ] and it doesn't wreck anything. 
S3: that's right um 
S1: so these are all the [S2: but ] capabilities in the system, [S2: just ] tha- those don't change what's c- what you're capable of doesn't change the only thing that changes is what's, what's wanted. 
S2: so you might wanna, so, if you wanna make that point then, and keep it this way then you have to point out, see the, just the graph, makes it look a lot more like the second example than the first example. so you have to point out that, the thing on the bottom isn't, commander it's just the, capability. 
S3: okay, mkay... um, so, (sorta) explain what the allocation is now a solution allocation is one where, one or more of the consumers actually acquire their goods and there's basically a complete supply chain all the way back to the suppliers. what that means is, well there's two things to, have a complete supply chain one is that for any good, the number of input arcs equals the number of arc- output arcs, or in other words supply equals demand. um, another requirement is any producer, that is selling its output good must also acquire all of its input goods, so, that is we r- require that the producers be feasible. and again here's another example of a, of a s- 
S1: you gonna explain the light green? 
S3: yeah i'll d- i'll do that right now. um, well maybe i'll d- i'll do it in a minute. so also i do have, i wanna point out there's this, producer here that is, colored light green, um, what i've i've done that to distinguish it from the other producers, um, this producer did acquire its input, but didn't sell its output. now that is allowed in a solution, it's not, uh es- the most, i- it's a little bit kind of wasteful to use some resources that um really don't, you know that are, that the producer doesn't want because it's not producing an output. but, we we need to consider this possibility, in in these, um solutions. and again i, showed, here here's the example again with the second commander coming in and shows how the um, how the, how the links change to feed the supply chain into the second commander. um, i wanna talk a little, go, back a little bit to the costs and values i that i hinted at. um i assume that, each consumer, is interested in potentially a, you know some set of goods, but, the consumer only wants to acquire one unit of one of the goods. um, so basically, (you know) it can acquire, some value for any, particular good but its total value is just the maximum of all those values of the goods that it obtains. the suppliers, um have some opportunity costs for supplying the goods, this can either be some real costs for, you know t- real monetary costs for um, supplying the good or maybe some lost value from some other use it could have put the, um, good to. so in this case i just say each supplier, its its total um, opportunity cost is the sum of of the individual opportunity costs for each good. um, 
S1: so um... uh you said you have a a, the quantifier of G and X in the second bullet you probably should have it in the first bullet too. so the max over G, should be G and X 
S3: here? 
S1: yeah. 
S3: oh yes, you're right. you're right. yep. <P :04> now, although this this may seem like a somewhat limiting um, um, set of, utility functions it turns out that, actually w- um with the consumer value, you can model quite a a large number of problems by playing some tricks with the suppliers. um, 
S1: producers 
S3: w- yes with the producers. and with the producers or with multiple consumers. if we wanted to actually model, um additive, um value with the consumers we can simply simply replicate the consumers and have each different consumer, um, want some different inputs and then, and look at, the, you know the the total, the sum value of them. um another op- possibility is maybe a consumer wants to acquire multiple goods, um rather than just a single good, well we can do that if we look at here, one way to look at you know this uh commander two is we can see that what it what the commander really wants is these three, separate goods and this producer, is basically, defining this good to be, the combination of these goods. so we can um, so we can actually have a, a large range model a large range of problems and value functions, with this simple um um, setup. um, now i wanna talk about the value of the overall solution. 
S1: (excuse me) uh uh, is the, second bullet is there a typo to have a C-O, on the left hand side and a O-C on the right hand side? 
S3: yep. <P :05> so first i'll say that the, the empty allocation where no agent where there's no agent buys or sells anything, i just applied that val- the value of that to be zero. now the value of a solution, is just the sum of all the the values of all that the consumers get, minus the sum of the opportunity costs, of all the suppliers in the solution. and, then, i define a globally efficient which you can also call optimal, um efficient is basically the economic term for optimal allocation is, um simply maximizes um, is is either a solution, or, a empty allocation which maximizes the total value. 
S1: let me just stop you for a minute Rob [S3: mhm ] so, just as a check, i mean i i i can't judge it because i'm too familiar, does this make sense to those those of you who are not so familiar? 
S5: 
S1: i think that's a good point and even i- even whether there's a slide or not, it i mean part of, what we're (referring) to is that you started so quickly, jumping into something that it wasn't, [S3: s- s- s- (giving some room) ] (it wasn't) clear so so so (we're) actually you know, maybe it's an introduction with that first thing, what i'm gonna give is an account of how these chains get formed, how to formalize what they mean, you know, [S3: mhm ] just what you're doing 
S2: why you're interested in this? 
S1: yeah, you don't want to bog down you don't want to bog it down [S2: right ] down too much, with the complete thing, but i think, you know that Stacy's point, is that, a- at least have some sense of what the, the heading is. 
S3: s- s- so say you know i'm looking at these task allocation problems where you form supply chains i'm going to start by giving some e- motivating examples then i'll get more, into the, actu- the the detail of how how i model and formalize the problem, and then and later talk about some of the mechanisms for achieving that? s- something like that (at least) 
S1: y- yes yes, if you express that content i think you would_ i- is that right Stacy would that (help) it? 
S5: 
S3: okay. 
S2: s- so getting back to your question about this slide? i'm pretty familiar with this but i'm, h- having trouble, understanding the math. i mean th- there's hardly any math there but, i think if maybe the symbols, or... or maybe just if you had a picture, for each of those two, 
S3: yeah i- i kind of... 
S2: i dunno i don't know but i i'm, [S3: i kinda went ] sitting here trying to figure it out. 
S3: i went kind of back and forth on that myself, um, yeah i could i mean i could_ this is a pretty simple concept i could just say, you know say this is the sum, this this is a little, nicer way to represent this... i i don't but in- may- maybe someone can give me, some suggestions i... how- is is is it the equ- 
S2: well, i mean in those two examples, those two equations X is not the same thing right? we're not looking at 
S3: um, n-... no that's, well i mean i can use some different letter to indicate it. 
S1: yeah but that would 
S2: but suppliers only supply one thing 
S1: no 
S3: not necessarily. 
S1: so it's so he has changed the model since the last time i saw it i think 
<P :04> 
S3: it it do- i mean it turns out it doesn't really matter whether they supply one thing or a multiple things because [SU-2: right ] it the the value is added the cost is additive across suppliers an- i- within a supplier and across suppliers, it it's really just a it's just a matter of, convenience in modeling some, particular problem. 
S2: sh- can you say again why, it's the max? 
S3: the max? i'm just [S2: good ] a- what what i'm assuming here is that, a consumer, only wants to acquire one good. 
S2: okay. 
SU-M: or, if that 
S3: o- o- o- only gets value from one good, and and we assume that uh i- if it ends up with some set of goods i- well i- it gets the value of the maximum good and all the all the extra goods don't acqui- provide any, further value. 
<P :04> 
SU-1: (okay) 
S2: but... consumers only ever (draw on) where it has inputs that, where it requires all of them. 
S1: no they o- actually in these all the examples is they only have, have inputs of one. 
S2: but if they had multiple inputs it would be that, that the meaning would be they ha- they need all of them, [S1: no ] just like any other (xx) 
S3: no well now i'm showing here, so this comman- so this commander, well, um, you know, yes it it does want all of these inpu- you know you can look at it and see if (you want some of these but) 
S2: so, that agent the ground attack requires all three of those inputs. 
S3: all three of those 
S1: that's a, that's a producer. 
S3: but this is a producer. the commander only wants this, (in) wants this good. 
S2: well [S3: which is def- ] yeah but if you had a commander drawn that had, two in- incoming goods, 
S3: that comman- has [S2: to be consistent ] two incoming goods that it it's trying it says, i could either have this good or this good, i don't really care to have them both. having them both doesn't give me any extra value. 
S4: so maybe you need a different shape, for that so cuz i- 
S2: yeah 
S1: actually actually even better, why don't you just, have consumers just take one good. period. right none of your examples, 
S3: no i do have an example with the time [S1: oh you do ] dependence 
S1: oh, see that's what i meant. 
S2: but, but i- see you've changed it cuz it used to be, i mean, it's easy to picture what a_ c- consumers, are just like everybody else except they have no output, i mean that's, the semantics of the symbols and stuff and, suppliers are, just like everybody else but they have no input. [SU-4: yeah ] right? but, but now if you're allowing, commanders or the commanders the consumers to have an or relationship over incoming arcs they're they're much different than, the producers. 
S3: yeah, they are. 
S4: so they sh- you should have a different shape i think 
S2: yeah 
S3: um yeah, you're right, um i used to- i, i- it's really the limitations of the drawing program that caused me to d- 
S4: well ugh 
<SS LAUGH> 
S3: i mean i_ well you see_ wha- in my in my_ no, in my papers i i i i ha- was able to draw nice oval, scr- 
S4: no, that's true PowerPoint has like, [S3: yeah you c- ] thirty shapes. <SS LAUGH> (xx) 
S3: yeah none of 'em w- none of 'em_ none of 'em matched well with what i, was had, traditionally had in the paper, but 
SU-M: (xx) 
S1: so i_ i think i dunno, i think the fact that it's all the way on the right and has nothing outgoing is is enough of an identifier and i also think it's okay for it to be different, it is different (it) has a different bidding policy, um, you know it's not like it's a special case of uh 
S2: you you should use, different symbols 
S3: no, ok- well no one thing one thing that might clarify things maybe i should wait on these values and costs af- until after i do scheduling because here, this is where it becomes really clear why a, a commander m- a a consumer would want multiple, to consider multiple inputs. 
S1: um, yeah, and it doesn't seem like that stuff at all refers to values and costs, the scheduling, those next two slides of scheduling right? 
S3: not no, not explicitly 
S1: okay so since they don't... uh uh good why don't you (bring that in there) 
S3: okay, i can change that order 
S6: is that cuz i was just gonna, ask why it's not the case that, the, consumers and suppliers are not special cases (in the first place) is that something that should be clear by now or is that (coming later?) 
S3: well um, well, they're not special cases of producers because, see a producer, i mean i- i'll get into this later but a produ- consumers and suppliers can get away with really, really s- like, really simple, bidding policies and, it's a little more, complex for the producers because they have hafta they hafta get apart all their inputs in order to sell their output. 
S2: wait why couldn't you define them to have, potential to have or relationships over inputs too? 
S3: the, producers? 
S2: yeah. 
S3: you could do a lot of things. 
S1: you just replicate you just replicate, that it's easier just to do to replicate producers (than to do that...) it's true there are choices that you could have made other ways [S3: of course ] and they would have been, wound up being equivalent, um in the end, but i don't know the reason i f- don't have an intuition problem is because we_ producers and consumers always, uh typically are different. uh, you know that that there's cer- there's a qualitative distinction we make in, in their, values and their poli- and their uh, policies so, uh... that's not a problem. 
S4: yeah that's not a problem but i just think, producers and consumers have should have a difference icon representation (you know) 
<SS LAUGH> 
S2: they should because, uh 
S4: because i k- sort of forgot which was the consumer and which was the supplier. 
S3: le- let me s- let me see if i can rep- let me see what i can do about that later. alright. in terms of wha- so (xx) 
S2: especially if the in the graph, the arrows are gonna have different meanings, depending on which box they're coming into. 
S1: they don't have different meanings. 
S2: well, yeah multiple inputs to a consumer to a prod- yeah consumer, have an or relationship but multiple inputs to a producer have an and relationship. 
S1: no but that's not what the_ the arrows just mean, can, you know can make use of or um, you know an arrow from a good to a agent means can make use of. and whether it's, you know what the combination rule is, inherent in the type of uh 
<P :06> 
S3: so, let me go on t- uh i wanna, spend a l- i mentioned that this is task allocation and scheduling, and i wanna sh- um su- suggest how we can actually use this model to d- perform scheduling, now there are m- this is not necessarily the only way we would do scheduling but it it's certainly i think that it's a fairly general approach, um i'm assuming that uh, we're h- we have discrete time scheduling where, we have some hori- some some range of, of discrete time slots that we would want to schedule, the um, the goods over. um, the key point here is that we multiply the goods, times the number of time slots so we_ the airfield output, it can be available at time one two three or four. and, now there are certain times where, we may want to make use of, multiple units of an airfield maybe two consecutive time units of an airfield in which case, we have arbitrageurs, um, which will um, an arbitrageur will, take some number of consecutive inpu- uh consecutive um, time units for some good and produce a temp- what i call a temporal bundle good. so this good represents, two time units of of airf- of an airfield, um ending at time two. and this one represents two time units ending at time three and so on. uh in this model i assume that the fighters wanna, acquire, wanna acquire the- one of these these bundles they don't care which airfield they use but they wanna acquire both of the units from the same airfield which is why i've split them off in this particular model. um, i'll 
S4: uh, quick question, couldn't you combine T equals two T equals four, to- together, to make a, to make a bundle for two units, ending at time four? 
S3: it depends on how y- what how you're putting it's 
S4: oh you (mean) consecutive. 
S3: in this problem i'm assuming we want consecutive, um, y- you cou- there are a lot of ways you could model, scheduling depending on what your constraints are. i- i'm just showing, ch- giving a feel for how one might do this. we get 
S2: so why why did you choose to... let the fighters, get stuff from either airfield now when they, were kinda stationed at an airfield before. 
S3: well i'm i'm just as- i'm just saying well l- say for this problem they can i- i- pr- prev- previously they could get it from actually from either one-A or two-B, that was the case before, if 
S1: one-A or one-B. 
S3: one-A or one-B. there's also two-A and two-B down here somewhere, [S2: oh, right ] but i'm assuming that, whichever one they get it from they have to get it from, both of their units from, from the same A or B airfield. 
S2: okay. 
S1: um, what's that, little box? before the word arbitrageurs? 
S3: that was a conversion problem, from PowerPoint, whatever i had before to PowerPoint what you have here. 
S1: what was what was there? 
S3: there was nothing... there. 
<SS LAUGH> 
S3: like a sp- there was a space or something. 
S2: some kind of control character 
S1: okay. i see what you're saying, um, it might be clearer i- if th- that label two-two, maybe, if you, since you have room what if you just spelled out airfield, parentheses, two-two. 
S3: yeah i think you're right i c- there is room for that 
<P :07> 
S2: what does, A-T-T mean under the fighter attack one? 
S5: 
S1: yeah that's another thing yeah 
S3: at. at, yeah, um it's 
S2: oh, that's a 
<SS LAUGH> 
S3: at T, yeah, oh, i put so- 
S1: what- another thing you might do is italicize T. 
S3: okay. 
S2: although if you're gonna do it in a [S1: yeah if you (xx) ] from a computer. on the compu- from the computer it doesn't look as good (as it) (xx) 
S1: that's true 
S2: it can be hard to read 
S3: i'll i'll play with that to make it, better, might put the at back up, up here 
S1: write an at sign or something, instead of A-T 
S3: mkay. now i also wanna mention that sometimes when we w- go into scheduling we don't want to make all the goods we don't wanna make them all temporal goods like this, um, i'm assuming in in this problem, um that the fighters, we- we're just scheduling the airfield over some short period of time, but once the fighters go out they take several hours to perform their, their attack, and that's beyond the scheduling horizon. so i assume that actually the f- using the fighter squad, tha- tha- i s- say that that's actually consumed, and you can't use, the same fighter squad over multiple time periods. so i don't multiply this, time four times i can just have a single unit, of it, and to perform a fighter attack you have to acquire one unit of it, and this guarantees that you_ only one of these time slots, can, can actually be active. for the fighter attack. 
S4: w- why do you have a, another good at the very end? 
S3: at the_ why do i have these? 
S4: yeah 
S3: this represents a fighter attack. at time two, at time three and time four, which a fighter attack requires use of the [S4: no, i understand that ] fighter squad, and also the airfield. 
S4: doesn't that, s- rectangle represent a fighter attack attempt? 
S3: this? this is, well this is a fighter attack producer. [S4: producer... i see yes okay ] that, that y- 
S4: so you don't have a consumer in this example. 
S3: not not okay i'll i'll get to that, it's it's too big to put on a single screen. [S4: okay ] i- i- i'm s- i should have mentioned that but this is only a portion of the network... 
S4: okay 
S2: i don't know if this would work but if you could, like take the previous network in a little box up in the corner and, and draw, put, you know some color on the part that you, exploding, that might, help place it <LAUGH> 
S1: i'd say i'd say one thing we could have learned from (Porpidses') uh talk yesterday is all the, [S2: yeah ] uh, animation techniques that 
<SS LAUGH> 
S3: i might be able to do that, um, 
S2: i don't know if that, would work but it would help u- help us transition to this, chunk. 
S3: i certainly should explain up front that this is only a portion of the network. that's something i f- i neglected to do. um, now this is at the other end of the network a portion of the other end with with commander one, um actually yeah this's commander one and i- and it wants an air attack, and w- it's happeni- it can have the air attack at time two three or four. and we might assume that the commander has a different value for acquiring, the air attack at the different times maybe earlier is better, or maybe we could even say that, you know aft- at time four is too late and we might have a zero value there, for instance. so, um, and then this is where i, go and talk about the values again. um, 
S1: not again, but for the first time 
S3: or- or i instead <SS LAUGH> so i just talked about values, now, you know 
S1: s- so i see oh we're not gonna, get back to scheduling again after this right? is this 
S3: not explicitly [S1: okay ] this the p- okay so i should_ i'm sorry i- what i should say i- so the point here is that i've modelled scheduling within the same framework as, as the s- as the as the as basic task allocation. so any result i prove about the general task allocation model will, by definition apply to the scheduling also. so um, this is an- this is- this shows that i have a very general model and, and, i can simultaneously do the scheduling and the task allocation. so i'm going_ g- in general i'll be focusing on, the basic task allocation model without looking at a any particular scheduling problems generally because it takes too much space. um, so i've talked about the, you know what a a va- you know a a an efficient solution is in terms of the value, to the agents, um, what we want to do, is to somehow form- you know, construct these solution supply chains, and we want we wa- want and and and preferably we'd like to have very high v- value, um efficient solutions. um, the question is how do we do that? we can certainly do this in a centralized system using various 
S1: did you, y- you know in that talk about value do you have you don't have value of a solution yet. 
S3: i talked about, yeah i did. 
S1: oh you did? 
S3: yep 
S1: oh you did. [S3: yep ] okay you had that [S3: yep ] okay i'm sorry. 
S3: that's that's why it probably works better, [S1: yes ] up here. [S1: yeah ] so um, so we can certainly do this in a centralized solution using various and or search techniques, but i'm assuming that, we actually are working in a distributed system, of s- um where you know p- these agents are actually, you know autonomous units, that have their own local information, and we, they they aren't aware necessarily aware of the whole system and their maybe, don't want to reveal all their information to the whole system, um directly. so, 
S2: is it_ do you have any good reason to argue that that might be the case of, the, um military, application? 
S1: well i don't think you'd wanna argue specifically in [S2: no ] the military you want to argue that it's r- relevant to, s- to some, uh, common applications. 
S2: right, [S3: it's uh ] and it- it's a little, ironic that you choose the military as the example when, they have a much more hierarchical 
S3: remember the military's the one giving this money 
<SS LAUGH> 
S2: right. [S3: um ] but i don't know if you'd wanna, say something about that 
S3: so i i i wanted to sidestep i i do want to sidestep the issue of w- un- under what conditions you do, take a decentralized approach. I'm assuming that there're some, either social or technological constraints that really require we take some distributed, w- (that we) that our solution approach be distributed in some way. and, what i want to do is look at well what's the_ how far can we go in doing this, i- in in solving this in a decentralized way. what is what is kind of the extreme, decentralized approach to this? um, and the economic answer to that is, to introduce a price system. and what a price system is is it just um a p- um, assigns a nonnegative number to all the goods in the system, here are just these, numbers with the dollar signs next to the goods indicate prices. um, what these, what the agents do_ what these prices do is indicate the relative global value of the various goods, um as compared to the as compared to the other goods. and, the agents then will use the this local information of their goods of interest and the prices thereof to guide their decision making process and determining the final allocation. um, so the question is, so how how do the how do the agents use do this? what what are their incentives to um, to tr- what are their incentives in this price system yeah? 
S4: y- you have prices on, suppl- on um, producer_ <SU-M LAUGH> wait, consumers and suppliers, that, you didn't um explain 
S3: okay, may- maybe, yeah maybe_ okay so um yes, the the the values i put on these agen- on on the consumers and suppliers represent their values, the- these numbers and while the numbers on the goods represent their prices. um, i im- by placing the, a dollar sign both on the prices and, the values i'm implicitly saying that the values and the costs are represented in monetary units. so basically on the same scale, and i'll and i'll explain that exp- i'll i'll formally explain what that is here 
S2: maybe maybe you would wanna, back on its side put V, [S3: value E ] V equals ten dollars or, something 
S1: right no C equals two three, [S2: yeah ] you know on the on the on the left side. 
S3: okay 
S2: something like that. 
S3: uhuh that's a good idea 
S1: yeah (that'll help) but, also do you want to say anything about, you know like pointing out that uh, uh, the ground attack makes a profit, and that commander two is happy, and you know i mean without, [S3: s- ] going through the whole thing? you know 
S3: so, (lemme say) i was goi- i mean i could talk about that, [S2: (i don't, b- but) ] so i was gonna talk about it formally here, maybe i maybe it's good 
S1: it might've helped to have given an example just look at this eyeballing the network first and then... 
S3: that's a good idea 
S2: is that paratrooper one supposed to be green? 
S3: paratrooper one, paratrooper one, that is a bug, i'll get rid of that... no no, that isn't a bug the um, it_ what is the fron- yes, tha- that's a bug, that's not green. thank you. so, what's going on here? well, the s- so how these agents use these prices t- to guide their decision-making? well these these, consumers, want to um, acquire their in- acquire a good, at a price below their value. so you can see that this commander's, um ha- i- is a is acquiring its its input good for twenty-two dollars which is less than its value of thirty. and the suppliers on the other end, are willing to sell their good if they can um, recoup their costs, a- at least recoup their costs. now the producers in the middle don't have any intrinsic value for the goods so what they're looking for is just strictly profit, they they're willing t- they they'd be willing to be active in the solution if the um sum of their i- if their output co- um value, their output price is greater than or equal to the sum of their input prices. and this is just um, a formal statement of that um the agents are_ ideally the agents would want to maximize their surplus, where the surplus is defined as i specified, it's basically the difference between the value they get and the costs incurred. <P :05> so the in, the journal-equilibrium approach, um the kind of the ideal situation is to end up with a competitive equilibrium, through some m- you know somehow to get a c- competitive equilibrium what this means is, simply that, um there's a set of prices, such that the_ an- and an allocation such that, the agents get an optimal surplus allocation, at the equilibrium prices. um what this means is, the consumer, will get the single good that maximizes its surplus, the different_ so the the the maximizes the difference between the value of the good it gets and the price of that good. if it gets any other goods, in this model, those the prices better be zero because they're not any_ adding any extra value. um, a supplier will simply sell each good, that_ for which it can, um get, acquire uh work_ that it can sell for a price higher than, the value for that good. and the producers, will buy all their inputs and sell their output if they're profitable, um otherwise they, wanna trade nothing. and so, tha- that's so this includes both the um, the, optimal, the optimality constraint and also the fe- the feasibility constraint i talked about before. and also would require that, supply and demand be balanced. 
S2: but i- uh someo- some producers are at a, negative value, [S3: that ] they can't have that 
S3: then that's not an equilibrium by this definition. 
S2: oh. 
S3: so, lemme talk 
S4: do you need to explain the, uh competitiveness assumption? are you making a competitiveness assumption? 
S3: it's kinda, well it's implicit in this, i- i'm i'm not talking about any_ i'm not talking about_ competitiveness is be- whe- is when you're talking about behavior, i'm not talking about behavior, the only assumption is here is that they're optimizing with respect to prices only. 
S4: the current prices so 
S3: right wi-with respect to some set of prices. i'm not i'm i'm uh sidestepping the issue, of how you would get a competitive equilibrium right now 
S1: right but di- but what makes it a competitive equilibrium is that everything is relative to given prices, and that's, stated, [S2: yeah ] you know there. 
S3: right. so what are the_ so, here's an example of a competitive equilibrium. um, um, in this case, um you notice that for all the green agents, they're making a positive surplus, or a nonnegative surplus at least so for instance this agent, um its its output is six-dollars-and-fifty-cents, and its inputs are six dollars, so it's making a sixty-s-cent profit, a fifty-cent profit, and it's willing to, be active. 
S1: so tho- those are A B to E 
S3: A B to E yes that's 
S1: and same with B C to 
S3: yep 
S4: B D 
S1: <LAUGH> B s- B C D to E 
S3: yep. 
S4: and then just E to F 
SU-M: yeah i guess you could (xx) 
S3: no, D E no no it's it's the D E to F 
SU-4: why oh yeah 
S2: just go through all those bullets and make sure they have the right labels 
S3: yep yep 
SU-M: yeah 
<SS LAUGH> 
S3: okay, um, so so thi- so for instance this agent is profitable. <S2 LAUGH> this agent, um has the input costs, i- input prices are totalled to seven but its output is only six fifty so it wouldn't want to take part in the solution, so therefore, you can see that it's excluded. <P :04> now, just by definition, the equilibrium is stable with respect to prices. um, another important aspect 
S4: wa- wa- wait what does that mean? 
S3: i- it's stable with respect to prices meaning the agent no agent would want to um, do anything differently, at the current prices. 
S4: unilaterally 
S3: um, unilaterally, actu- actua- yes. no individual agent would want to, deviate from the allocation it receives, it it couldn't do any better at the current prices. the um, equilibrium is globally efficient, so, what this means i- um i- in thi- for this model, when the agents optimize locally, we're also optimizing globally, and this is due to the fact that they have this qua- what we call this quasilinear value, which means they, they value, goods in their value is l- linear in the money, the amount of money they acquire, and that means they can transfer the utility on a common scale 
S2: so so you know that, only, the only, competitive e- equilibrium prices that exist are, are, the efficient prices, or support the efficient allocation, there's no, inefficient, c- equilibrium? 
S3: equilibrium is, globally efficient. i- it any, [S2: yeah ] there may be multiple equilibria but any, equilibria you can you come up with, has to be globally efficient. 
S2: but that's not, necessarily true for, all discrete, resource allocations 
S1: no it's true for this model, you want to point out that you've [S3: it's, true for this model y- ] proved it, in your proposal, [S3: yep ] there's a proof of this 
S2: okay 
S3: y- y- yeah, i i proved it for this particular m- model, you could, you could come up with different value functions for which that may not hold true. 
S2: okay 
S3: and, and, and a- as you know, bundle-pricing schemes. um, als- but unfortunately, an equilibrium actually may not exist when you have, the discrete goods in complementarities which we, do have in this problem. i'll show you a particular example, of ho- where you may not have equilibrium. um, basically, what what i showed here are the constraints on the prices for all the goods, um, this constraint 
S1: so so first of all what's different from this and the previous example? 
S3: okay, the the only difference here is, that the consumer has a lower value. um, yes i'll maybe explain that so, this is showing, 
S2: what was it before? 
S3: uh, i think it was fifteen. um, now the the key to h- here is that, the total cost for the solution is um, is seven, and the consumer has a value of nine. so it_ i me- if we were to have an equilibrium, it should be this solution because that's efficient. however i'm going to show that we can't have an equilibrium if the consumer has a pr- value this low. and the reason it_ so if we have, we look at this, um, um, constraint, this is to ensure that, that this agent is profitable. on the other hand this, constraint, is to ensure that this agent, is not profitable, because if we raise this sufficiently high, um then this agent, can't make a profit on there. well what that means, that if you take these two constraints and (keep) them together we have, that price the price of F has to be greater than or equal to eleven. so even though, um we_ the, um, thi- this solution, would be e- this particular solution would be efficient for the consumer having a value range from seven_ from anywhere above seven, we actually can't have an equilibrium if its value is below eleven. 
S4: well the the consumer shouldn't be green, i don't think. 
S3: no i'm just showing, i'm saying, this is what the allocation would be, 
S4: oh the green is the, [S3: i'm i'm just ] is the optimal allocation but 
S2: so that 
S1: oh it's just a solution 
S3: it's just some it's it's so- it's a solution allocation, that, that it happens to be the optimal one. 
S2: so the [S4: (yeah but) ] minimum cost of the solution is really seven. 
S3: ye- yes [S2: i don't know, if that's your right, the terminology ] the if the consumer had a value as low as seven, we would still have_ it would still be efficient to_ this solution would still be efficient. however, we_ for for c- for a certain range of consumer values, we can't get an equilibrium. 
S4: and the way you, explained it was, you know that price has to be high enough su- such that the supply_ um, the producer was not active [S3: correct ] but um, why is it the case that we don't want him to be active? 
S3: because if this [S4: i mean why do you want to force him to be ] w- w- well first thing, we have to remember, this this producer, has to acquire this input. [S4: right ] so that means that, this this producer cannot_ should not be allowed to, [SU-M: (xx) ] so that therefore this producer has to supply this input since this_ and therefore this producer shouldn't end up buying anything, it since it, since it can't buy this, it shouldn't do anything at all by the equilibrium conditions it sh- either, sell its output and buy th- all its inputs or else do nothing. that's the only way to have a solution here. 
S7: i get it. the constraint on uh, price of C, should that be greater than or equal to one? 
S3: no less than or equal to one because, we don't want this supplier [S7: okay ] to be active. 
S2: you might_ you could put, for the consumer's value V between seven and, eleven. or i don't_ i mean f- so what you're saying is for any, value in that range, there's no equilibrium. 
S3: yeah, y- that might be clearer just to say, well 
S1: so actually w- i'm not sure why it's the the uh constraint, why is it greater than five, because the price of C can be as high as one, in each case? 
S3: well it can be okay but the higher that this is, the higher um let me see <P :06> you're right, so this could be 
S1: so D can be as low as four, really, and still exclude 
S3: it could be as low as four. it could be as low as four, you're right. 
S1: so it's really only ten now, i mean still 
<P :13> 
S3: yep. though though i'm ac- yes. so, so s- equilibria don't always exist. now now i have, b- sometimes they do and sometimes they don't. the question is, when they do exist, how can we reach them and wha- you know what do we do when we don't have equilibria in, or can we even always each reach equilibria when they exist? um in the auction theory literature there's been a lot of work looking at price-based auction mechanisms that try and, reach equilibria or some approximation of equilibria sometimes you can't, reach it exactly, or o- and when they when they don't each reach equilibria the idea is to hopefully have, produce an allocation with a, sufficiently high um, wi- with a fairly high efficiency. um, one common approach to this, um using these priced based methods is the simultaneous um ascending M-plus-first-price auction. and this was actually used for the um, F-C-C um radio spectrum auctions a few years ago. um, 
S1: really, was it M-plus-first-product? 
<SS LAUGH> 
S3: i'm s- okay i i there was_ you're right, it was a simultaneous ascending auction, this this is a variant of the type of auctions that were used for the F-C-C auctions. 
S2: they had a lot of other rules in there too, right? 
S3: right. so this is a variant, it's not exactly, the same. 
S1: so when you say often used say simul- just simultaneous [S3: yeah ] ascending [S3: yep ] auction [S3: right ] and then this and [S3: we're using a parti- ] then that's commonly used and here's our 
S3: yep. we're using a particular variant with a an M-plus-first-price auction rule. so there's an auction for each good. um, to kee- one important point is these auct- this auction is two sided. both the buyers and the sellers will bid in the auction. and, as an iterative asynchronous auction, that runs um, you know according to this bi- you know high level structure. um, first, some agents bid, and whenever an auction receives a bid, it issues a price quote. and, then, um then maybe some agents when they receive that price quote will decide to change their bid, in which case the auction will submit a new price quote and re- repeats this continuously, until, the agents stop bidding. at which point we've reached quiescence. 
S1: so, that's kind of weird but what is it what is the bid this is supposed to be the program for the auction? 
<SU-M LAUGH> 
S3: um, this is really the protocol for, the agents and the auc- the interaction between the agents and the auction. i mean i- i could say a received bid 
S2: y- yeah you could say received it 
S1: so how about how about, just, instead of repeating anything, how about you have a loop that says something like until quiescence, on bid, issue price quote. <SS LAUGH> uh, and then, clear. 
S3: (on bid) 
S1: (well but wait) the point is it's event driven. the auction [S3: okay ] from the uh the auction is completely event driven. it receives bid when it receives bid it's uh does something [S3: right right right ] and then, when quiescence, is reached it exits that, event driven mode and just does something. 
S3: okay. i'll agree to that. so tha- that continues until the agents stop bidding, at which point the auction's e- the auctions will clear. and the clearings determines the final prices for the goods, and, actually i should explain what the price quotes are i think i, glossed [S1: yeah ] over that and, um, so, lemme go back so, lemme lemme, rephrase this so, un- until_ so the auct- th- the, whene- whenever an auction receives a bid, it will issue a new price quote. and a price quote, basically provides some intermediate information which um, specifies the um, w- what the prices would be now based on the current state of bids. now of course, this is subject to change because once the agents receive these price quotes, they may want to submit new bids. so, um every time so every time the agents do submit a new bid the auction then submits a new you know releases a new price quote. and this continues until all the agents stop bidding, at which point we're at quiescence, w- what i call quiescence. when this is finished the um, auctions will clear. and a clearing, ba- it determines the final prices, it determines an allocation, which specifies which agents get what. now throughout this bidding process, the auctions um, require that both the buy bids and the sell bids must i- increase. now this is a little bit different from standard auction au- much of the auction literature, um where only the buy bids must increase, but we do find that, um requiring both buy and sell bids to increase, um is is important for pr- um proving some of the conversions properties we, achieve. 
S1: it's different mainly because most, most ascending mechanisms ther- are only one sided. 
S3: that's true. [S1: so ] well there are there are some, some, there are some, two sided options where the, sells must go down and the buys must go up, but. um, anoth- i don't wanna go into too much detail about what's involved -volved in the clearing but the important point is that, the auctions balance the reported supply and demand, at unif- at a uniform price so each auction ha- specifies a single price at which all the agents trade at, at that auction. now this is a, very complicated problem to analyze um, you know the ideal s- um, sit- you kn- tr- tr- traditional s- approach would be to, um, calculate a Bayes-Nash equilibrium on behalf of the_ for each of the agents and assume that the agents behave rationally a- according to a Bayes-Nash equilibrium. unfortunately doing so is k- is kind of beyond the state of the art, and, and for something this complex, so we are simply assume that the um, the agents use some very simple bidding policies, that do obey the ascending restriction and also can obey the decentral- tr- decentralization constraint in that the agents only, consider the goods of direct interest to them. so the suppliers, um simply bid their fixed i should change that to cost they they simply bid what their costs are, for their goods. and um, and a consumer, will, um, start by bidding zero, for all the its goods of interest and whenever it's losing, whenever it's not winning a bid, it will raise, its bid on on one of its goods of interest that wi- would maximize its surplus at the current prices and it increments it by a small amount. um, the, producer, is is the the interesting agent here as i mentioned, for its output i- 
S1: i'm sorry it, it increments beyond the current quote 
S3: y- yes, a small amount beyond the current price quote. [S1: okay ] the producer will bid for its output the sum of its, current of of the current prices of its inputs. and it will also add in a small increment for each input that it's currently losing. and that's under the assumption that, if it's losing an input, it could actually win it if it bid a little bit higher than the current price. um for the inputs, a producer will start by bidding zero, and then will increment its a bid on an input whenever it's infeasible, that is when it's, winning its output but losing that particular input. now sh- i'll give you a concrete example of the producer here. now this is a producer um, the prices are specified here in the current bids, the green arrows indicate bids that it's currently winning, and this red arrow indicates the bid that it's currently losing. so, the producer has no reason to raise its, input bid on A, because it's winning it. however since so it holds that pr- bid at two. however, the producer is, winning its output but losing this input. so it would raise its bid on B, to two. um, for its output it will bid the sum of its input prices, two plus one, and it will also add an increment on, f- for this, bid for this bid, because it's losing it, so it will bid a total of four. here i- i'm i'm assuming that it it has an we have an increment of one dollar. 
S4: then, why is it that the, suppliers and the, consume- the, suppliers and the producers when they're selling things they're not, doing anything strategic they're just bidding their top valuation. 
S3: you're right i_ well, okay the consumer [S4: well ] doesn't just bid its top valuation it kind of it slowly increments. 
S1: no you said supplier s- 
S4: no no s- when they're when [S3: but ] they're selling. 
S3: the prod- the the supl- the consumer doesn't, isn't 
S4: no the producer when it's selling 
S3: the producer when it's selling? 
S4: it's just the sum of its input, it's not trying to make any profit, it's just 
S3: you're you're right i'm assuming, i'm i'm kind of ignoring strategic issues here. um we could look [SU-M: well ] at, situations where, a, um, a producer would bid for its output some linear_ say some linear function of the inputs, and actually everything i prove, um, w- would still follow, based on that, i- if, wou- would st- would still follow for that modification, some of the empirical results i i show, would definitely be altered by, that k- sort of profit, taking 
S4: it just seems that the producers, are trying to get the lowest possible price, for the things they're buying, but they're not but they're just trying to sell it, for no profit at all and also the suppliers [S3: s- ] are just trying to sell things, for no profit 
S3: so so for no profit well, they're saying that_ what they're saying is that no, in this case no profit is, good enough, they may end up getting, [S4: yeah ] positive profit. 
S4: it, are they, is it incentive to_ it's not incentive dependent? 
S3: yeah, it isn't, s- i i, that's something i want, to address in this thesis propo- in in this in this work is actually, looking more c- careful- developing a m- a better a good model of the agent incentives and trying to, analyze a little bit more carefully what the agents might really do 
S1: so but it's not as bad as it_ the fact that it's M-plus-first-price, does, um, reduce the, uh, disincentive for, uh, bidding to sell at your, actual costs. 
S3: Ronnie? 
S7: um, in, an earlier result is that the M-plus-first-price auction can d- that, M and M-plus-pla- M-plus-first-price auctions are incentive compatible for buyers or for sellers one is compa- it's (xx) 
S3: that does not hold in an iterative, m- if you have iterative auctions 
S7: oh okay so that result is 
S3: right there there are n- 
S7: so so y- there may be incentive compatibility for, uh, say both buyers and sellers in each auction. 
S3: no we we shouldn't expect any sort of incentive compatibility. 
S1: yeah it only makes it worse when things are iterative 
S3: w- well another thing is it's really hard to talk about ince- you can't talk about incentive compatibility for the pruc- producers anyways, you can only talk about incentive compatibility when you have, a a, a set value for a good. the producers want to make profit. and, it_ that_ they just have an extreme- a very compli- 
S1: no no you cou- no you could talk about, a strate- an incentive compatible strategy. 
S3: well if you fixed, i mean if you fixed any, all but one, the price of all but one good, you could talk about well i- what's the incentive for bidding on the other one but i- [S1: oh i see ] if the producer knows that those prices are dynamic, 
S1: oh i see, the producer <P :05> right 
S4: but but this is not an iterative_ i mean, the price quotes are iterative but it's not an iterative auction it's a one-shot_ i mean only once (do) (the things) 
S3: it only clears once, [S4: (right) ] but it's iterative in that, it it, provides intermediate price information. and that really 
S4: and that in itself (xx) 
S1: the actions, the bidding actions, 
S4: okay, that's what eliminates, incentive (xx) 
S3: yeah 
S1: yeah so actually maybe you're right there is a weird thing because, this isn't a direct mechanism where the producers just report their types actually if they did all they would say is, here's my inputs and here's my outputs, [S3: correct correct ] that would be the only information. 
S3: correct. 
S2: um, i was wondering is there some, way you could, describe the producer's, um, bid on his output as a function of the price quote? like, it can only raise it, if, if its, you can imagine that if its, ha- if its costs are greater than, the current, um, uh, bid price i mean, than any buyer's willing to pay, then it might choose to just raise it as little as possible. but i- if it's actually less than some buyer's willing to pay, it could, raise it up to that, that price, and that would be profit maximizing, a simple profit maximizing (bid.) and it probably turns out that as the network progresses, the consumers, never bid any more than they have to so that, it stays at this lower, the lower bound. so the 
S1: can you repeat, i did- i didn't get the, proposal (xx) 
S3: yeah 
S2: so an explanation for why this might be a reasonable strategy could be that, you could_ a simple, bidding policy for the producer would be to, bid, as much as anybody's willing to pay. 
S3: but you [S2: but just ] but they don't know what anybody's willing to pay 
S2: well there's a price quote 
S3: but no no um but um, what anybody's willing to pay, it comes from the consumers way down here. and that information slowly [S2: right but ] gets filtered back i- i- [S2: but ] indirectly. 
S2: in, f- yeah. so it's_ at some intermediate point, there is a price quote that says that, someone has offered, effectively someone's offered to pay this, buy it for this much 
S1: well you can't really tell that but there is a big quote. [S2: yeah ] you can't tell if it's from a buy or, [S2: right ] from a sell but 
S2: right so, but you know there's a buyer out there. [S1: right ] [S3: (right) ] um, so, so since you have a big quote you can say that, you could say that the consumer_ the producer will, offer to sell it, at that quote, or, [S3: you know but the th- ] or, if if their [S3: but the thing is, the th- ] costs are greater than that they just choose the minimal amount over that quote, hoping to be_ to (lay the win,) as the prices rise. 
S3: i think all all these price quotes are very, are tentative, y- um, i guess i'm still not... 
S4: yeah but you're assuming that they're taking prices as given 
S3: you're (just) 
S2: (i mean) the reason why they might not just set a big price, is because, they, want to try to w- sell the, the [S3: right ] uh, the [S3: bu- but you ] resources, and they haven't some information about what someone's willing to for it. 
S3: but but i what i'm assuming is here you_ when you bid for your output, it you're you're assuming that, you want to at least cover the cost of your inputs. 
S2: right so, but if the, if it so happened that, the bid price was much more than that, than the cost of your inputs, then, a reasonable strategy would just be to bid that. 
S3: n- well, no you could say a reasonable strategy is to stop bidding on your inputs, maybe but you don't you won't 
S2: no if someone's willing to buy it for a lot more than it costs you, you don't want to stop bidding on your inputs, you wanna, try to, capture that surplus. 
S1: but you would if the world ended today because it's an M-plus-first-price, auction, even by bidding your tr- your true costs... alright? 
S3: so if if the so you're bidding 
S2: no you're just selling, you're gonna, [S1: oh i see ] the buyer's gonna get it, you're not, you know 
S1: oh i see. that's right. 
S2: so, but so, so that seems like a reasonable story, [S3: mm ] right? but i, and i think it's also true that it turns out that, these bidding policies, make it so that, you're almost always, in the c- situation where you're placing your bid where, you're above, you have to_ because your inputs have increased, your new bid has to be greater than what someone's willing to buy so you, just do (as minimally) above 
S3: no not necessar- not necessarily. you don't know that they're gonna_ it may n- 
S2: not not their true value, but their current stated value in the pri- 
S3: it may or may not be higher than that. alright, you're winning all you kn- you know that you're winning this at some price, if you bid above that current pr- the current, bid price, that's because your costs, your current costs are, are too high. if you bid bel- if you bid below it then your costs are less than that and you're still gonna stay in the game. 
S1: so look at it this way, suppose that, uh, Dave and i are sellers and you're a buyer. we know that there you you've offered to buy at ten. and it costs me, three. [S2: right ] so i say, i know, i'm gonna offer to sell at nine, let's try to get more than (almost in) surplus. well Dave comes in and offers to sell at eight, and i can't lower the price because it's an ascending, auction. [SU-2: (okay) ] i'm, i'm screwed... so, that's one reason why, i shouldn't have gone right to nine i should have stayed at, three, and raise it to nine later maybe. 
S2: but if you were the only, supplier 
S1: well, but i have no way of knowing that. 
S3: and i and i well y- okay now i guess i'm understanding is you're saying, the bid all the way up well also you have to keep in mind that, that might work, okay if you're the only s- s- seller, selling to a consumer. but if you're somewhere in the middle of the chain, you bid up too high, on on multiple ends, then 
S2: well, yeah so, i'm, i think that, there's, there's some way to help explai- to help raise the intuition about why you might not wanna, raise your bid. why you wanna_ as a seller, and a producer who's selling you might want to stick to this simple policy. (xx) 
S1: so i i think i think it is hard to justify in the end, i think [S2: yeah ] you'd wanna just_ i mean the main justification is it's, it's myopic and simple. 
S4: well it's not really myo- i mean it's not optimally myopic it seems. is it? [S1: uh, ] i mean if the world were to end t- today, or tomorrow, would that be the optimal way, strategy? 
S1: i guess not because (xx) 
S3: um, no i i c- i can't argue that. 
S2: assuming they (have) both bid and (ask) quotes 
S1: well anyway i thi- we're actually, [S3: there, yeah, lemme ] running way late on the (xx) but but i think the point, i- it's a good point is that there the (the sheet of) issues though are really complicated and no you're not gonna be able to successfully, argue for it, you could, you know try some things but i don't know if it's probably not worth it, you might, 
S2: but some simple intuitions might 
S1: but they're wrong, the simple intuitions, you know they're they don't really, go through. 
S2: well but, but the first impression of the bidding strategy is just that it's so, natural. for sellers to raise their bids cuz that decreases their chances. 
S1: but what we know is there's actually lots of strategies, that, s- all seem plausible, and uh and some of them, don't work. most of them don't work and the one that Rob identified works and that's really, [S2: right ] interesting it's not because it's more, uh strategically appropriate than the others, at all. 
<P :05> 
SU-M: right 
S2: so, something... some justification even if it's just that, that, you know there's there are lots of other ones but they, we don't think they work but this one does, would help. 
S3: but, i'll s- i'll say up front and clear that there, are potentially lots of bidding strategies some of whi- some of which may work better or be more strategically sound in some, respect, we do know that this, does have some desirable properties and it's, it's why we've, [S2: for the system ] explored it in depth for the system. uh, now i'm i've talked about equilibrium before, um, i wanna_ you know i talked about a peer-competitive equilibrium there_ i've also defined something called a lambda-delta competitive equilibrium which is an an approximate equilibria, whe- where, the error from equilibria is, is, corresponds to the increment parameters in the bidding policies. and it turns out that this_ um the reason why i do thi- specify this is beca- when we have these discrete jumps, we can some- you know, you know it's it's pretty, impossible to exactly hit an equilibria, you may miss it by a little bit, um, but just intr- introducing these pr- you know these parameters and the concept, um, means we can talk about some_ you know equilibria we sometimes get close to. um, and this, this approximate equilibria is inefficient in proportion to the bid parameters. so i- it's it's it's suboptimal by by some bounded amount, which w- you know in proportion to these parameters. um, and it turns out that this this 
S2: what are the bid parameters? 
S3: uh i don't, [S2: just the increment? ] the the increm- basically the increment, the increment and the loss, a- and the input, the increment on your output and your input for the producers. and also consumers. um, and it turns out that this this bidding policy and the auction mechanism, if that, results in no, dead ends on the producer and a dead end is a is a producer that, buys some inputs but not its output. so if we have no no no producers like that, then we have this, lambda-delta competitive equilibrium, and it is an if-and-only-if, statement. now, even when we generalize this, n- notion of equilibria we're not guaranteed to reach, that equilibria, even when one exists, um, for two general reasons um, one is we may overshoot the equilibrium prices um, some of these you know this_ the price of this good goes higher than the minimum equilibrium price, um this agent is bidding hi- actually higher than eleven, here, because, of of the, that increment on its inputs. so we can overshoot it, and also as i mentioned we have we can have dead ends where this is what happens when you actually run the system, where y- you'd have a producer like this, that that buys an input but doesn't sell its output, so that's how we can miss the equilibrium. so since, since the equilibria, um, some i- is, since we we can't always get an equilibria i defined a somewhat weaker notion on prices called the valid solution, where basically all the agents in the solution have a nonnegative surplus, except for some producers may, may, i do allow that some producers may buy some inputs but not sell their output. 
S1: word, you have the word surplus twice (and not just once) 
S3: yep, thanks. so when we define this, we can talk about, some properties of this of this, bidding policy and, auction mechanism. um, because of the ascending auction rule, the bidding does always stop we always reach quiescence. um, if we reach a valid solution and the price of the goods for any losing consumer is higher than their, value, then we've, then we'll reach quiescence with a valid solution. on the other hand if we reach quiescence in at least some consumer_ at least one consumer's winning, we have a valid solution. um empirically i've also, um, based on uh, many thousands of experiments i i, i find that, if at least some consumer in the system values its, uh good high enough, that's relative to the other values in the system 
S1: so let's say, thousands of experiments it's really thousands of randomly generated examples [S3: thousands of random- ] (thousands) of randomly generated instances 
S3: okay, thousands of y- you know, about three-thousand [S2: (xx) ] randomly generated instances i find, find that i- if the consumer values a good highly enough, then the then a valid solution will form for that consumer... um, now i'm i talked about this problem of these dead-end producers that buy their inputs but not their outputs. we can improve the efficiency of the system, by allowing decommitment on those producers. and what that, um, basically means is any producer, that, that buys some inputs but not its output can decommit from those input contracts and then we recursively go back to the suppliers and basically cut off that portion of the supply chain. and as an example, what we do in this, what we do here is, we basically let this producer and this supplier, decommit from their contracts. and that would increase the efficiency, um, actually increase the value of solution by one-dollar in this case. and and in this case we would have the optimal, solution. with the decommitment. 
S1: and an equilibrium. 
S3: um no, it would not_ well if you_ not an equilibrium because you still have [S1: oh the supplier, right right right right right ] this_ because of the prices um, if you if you actually threw them out of complete consideration all the o- rest of the agents are in a an approximate equilibrium... um, i've done, um, i've done some more empirical analysis based on, um, over three thousand randomly generated trials, with a range of goods and, and and agents, uh i measured the fraction of optimal surplus and i compare- i compared the economy run with an A-star so- um search, and, the this protocol with with the bidding policies in in the auctions i specified, give a mean of, efficiency of eighty-three percent. but when we, include the decommitment, the efficiency rises to ninety-seven percent. uh, i found that ninety- about uh 
S1: yeah you really need to qualify those, numbers, to point out (xx) 
S3: i was i was gonna do that at the end, or or i i 
S1: i think right when you mention those numbers you've got to the o- the the next ones are l- are much less arbitrary so, i think it's worth pointing making a point with respect to these numbers. 
S3: mkay so one thing you do have to_ we have to be a little bit wary of, is remember that, um, you know i ha- i have this conjecture that if you if, some consumer, i- ha- s- values its goods sufficiently highly will reach a solution well we could, we could set some consumer's value to an arbitrarily high number, and know that we're gonna reach a n- uh a a solution, and there we could get arbitrarily high values, i- because i- you know, we ar- get arbitrarily close to optimum efficiency if if the if that consumer's value dominates all other values in the system. um 
S1: okay could you explain that so if the if the [S2: (and you did it?) ] consumer's value is a b- is a billion, then it doesn't really matter then the, the um surplus it's a billion minus, uh ten versus a billion minus nine [S3: right ] you know that's there's not go- you're not gonna be able to, measure much difference in that fraction, whereas, nine versus ten, is a, you know could be significant actually, it's not nine, but a billion minus ten versus a billion minus one, uh they're pretty much the same whereas [S3: right ] the cost ratio is still much more. 
S3: yeah so so we have to_ yeah i tried to design this experiment so that that isn't, a s- a strong artifact but, we you know we have to keep that in mind. um, i i did find that thirty-seven percent of the trials converged to the approximate equilibrium i talked about. and of those that did not converge to an equilibrium, the remaining seventy-three perce- the the remaining ones had seventy-three percent efficiency, and when we include the decommitment we had a ninety-five percent efficiency. so what this suggests, is that this protocol, is, you know it sometimes reaches equilibrium, but it st- it produces good results on average even when it doesn't e- reach equilibrium. 
S1: so do you have any sense of, uh what fraction can actually have an approximate equilibrium? 
S3: um, i do not have that i i haven't tried to measure that that that would that's 
S1: pretty hard, i know 
S3: yeah. so i i don't have that sense. 
S1: somewhere between thirty-seven and a hundred percent 
<SS LAUGH> 
S3: right, well we ce- yeah. now we certainly know that well, you know, a li- you know, a little more wo- th- um i guess i don't have i don't have the actual statistics here um, of of how many were improved by the decommitment but the- there, there was a, a good chunk of them were improved by decommitment, and so we we at least anything that's improved by decommitment, could have maybe had an equilibrium but we know we definitely missed it. well, actually i i wanna, i i don't i'm not gonna go there so so i don't know how many actually have an equilibrium. so yeah that thirty-seven percent could_ you know includes both the protocol, and, you know areas in the protocol, and also just nonexistence of equilibrium, in, yeah. 
S1: the sixty-three percent 
S3: yeah, yes. 
S2: uh those are the means do you have, uh what's the distribution like is it like almost all, a-hundred-percents and then a bunch of really bad ones? 
S3: it's, i- it's heavily weighted in in in in, in the ninety-percent and above region, very heavily weighted, um, basically, over ninety-percent are, of of the trials had ninety-percent or greater efficiency. the um part of the reason why, why these numbers are as low as they are is because there there's a good chunk of of of, results o- of runs that had negative, value. because so mo- there are more, there, so basically the cost overwhelmed the value to the consumers. and tha- and tha- and that's why, the decommitment was so useful, because it got rid of a lot of wasted, resource- you know, decommitted from a lot of wasted resources. 
S4: do you have any feel for how the, number of number of trials that converged to equilibrium varies as the size of the economy grows? (is) 
S3: no i don't. 
S4: okay. 
S3: i i it's really hard to measure the size of the economy, you know i mean, you can talk about the number of goods the number of consumers number of agents, then the interconnectedness some_ you know i showed you a very simple you know, small economy, with no equilibria, um, i- it's i i w- i thi- i i i didn't do that measure because i think it would, it would be misleading. a simple simple m- such a simple measure. 
S1: but wait i i would expect you know now reading the committee, Professor Dimmitt to, to push you a bit on the, empirical trial, part of things. 
S3: s- push me in terms of...? 
S1: why did you do this, instead of that, you know what could you have measured, what will you be measuring [S3: okay ] (xx) so [S3: okay ] (xx) 
S3: okay so, i've talked about, um you know w- you know the results of this, protocol. one there's one thing i've sidestepped is, how d- how do we know when when this, when we've reached quiescence? that's a straightforward thing to do if we're simulating this on a centralized system, where we know what the state of all the agents in the auctions. it's a, much more difficult problem when we have decentralized auctions and agents running on you know separate processes in a on an asynchronous system. um, the tr- the problem is that, local quiescence at one auction, does not imply global quiescence. so agents may have stopped bidding at one auction but there may be still activity going on in, other parts in the economy and if there's still activity elsewhere, prices could propagate back to that auction and there would be later activity. 
S1: so, so actually, it's not even clear what local quiescence means. 
S3: mm, so i gue- so local quiescence meaning, if a if a a particular auction hasn't received bids for, you know, you know, five seconds or whatever time period 
S1: well it doesn't mean that, (when they say quiescence) it means, i mean actually literally it means that no one, wants to bid, at the current price, [S3: right ] at the current state no one even wants to. [S3: right ] but they may but the point you made is that they may want to later, [S3: right ] based on a change in another. [S3: correct ] see what_ maybe something like, um, you know, current_ quiescence at a certain time, which you'll define you know later does not mean that it's gonna stay quiescent, that there's other auctions that are still active. 
S2: well you could say inactivity at one auction instead of quiescence 
S1: inactivity at one 
S3: yeah. yeah, i like that. 
S7: what about local stability? 
S3: i think inactivity, is, 
S7: (xx) 
S3: so, you know we could have time-outs and say you know, a- the auction could ask all its bidders you know do you want, you kn- there are a lot of ways you could you know check for inactivity but the point is, that's not a good measure of global quiescence. uh the trick is we want to have all the auctions reach con- (where they basically) reach consensus, on quiescence in a, and do it in a decentralized manner, we don't want to have some, centralized agent orchestrating all this we want to have the mes- the messages following the natural flow, in the task dependency network. i was gonna to give a high level view of how we can do this, um, one thing i do is when we have multiple consumers, i kind of there is some, sort of metaconsumer that, that i, introduce that, that is used to coordinate the consumer's activity so so we do have to have some, control over, we have to have some, knowledge about what's going on with the consumers but we don't have to look at the rest of the economy. um basically there_ when, when the con- when we have consumers, not me- wanting to change their bids they s- pass messa- uh a message called, that s- says, i'm quiescent. and uh, and, and if if the rest of the network is really quiescent also, it will, propagate back to the suppliers. um, but if at any point, new bids come about, um, the that message will not be propagated back and the auctions will wake up and continue their bidding. oh i mean the auctions will continue the price quotes and the agents will continue their bidding. um, one step those messages reach the suppliers if the if the suppliers are really, you know, are ar- agree that they are quiescent they don't have anything they want to change, they will say o- they'll send a f- a message firm, which sa- basically says i am firm, you know i'm certain that that i'm quiescent (key) locally, and agents and auctions will propagate that message back, to the consumers if they agree with that message, if if there haven't been any price changes or new bids. and once this, once this information propagates to the metaconsumer, the metaconsumer will send a signal saying, a clear signal, basically which will propagate to the network, and all the auctions will close down and clear. 
S2: you could_ does that consumer bid or anything ma- the metaconsumer? 
S3: all it does, all it serves is to pass these messages 
S2: maybe you could just call it a, quiescence detector or something, like that. using the word consumer 
S1: yeah metaconsumer, (xx) 
S3: yeah <P :06> now the- there are some restric- oop- a few restrictions on on on how this operates, i assume that messages, always get, delivered in some finite period of time in order between two agents, however i don't place, there's, i don't place any arbitrary time bound on them, on the messages. also i assume that the auctions know who their bidders are. so that they they know, whe- if they've received messages from every agent. 
S2: how do you know if you've got all the firms? 
S3: how do you know? basically y- y- an auction, will pass a message only if on- if it receives a firm from all of its, bidders. that's why you have to know who your bidders are. and the same with the quiescent, basically the messages, an auction passes on a message only if it receives it. it passes a quiescence only if it receives it from all its buyers, it'll pass on a firm only if it receives it from all its sellers. and turns out, uh given these assumptions with this protocol, um, auctions will clear if and only if, we have global quiescence. 
S4: there's a certain incentive for the, agents who are, you know buying something but they're not able to sell it that may not want to send off a firm, message, you know 
S3: so, the- so there's another issue, do agents wa- want to actually participate in this protocol. [S4: right ] and that's something, that i need to look at, in in combination with the incentives for the bidding policy. um, we can prob- uh what i'd like to do is, perhaps we can combine this quiescence detection protocol with with the decommitment protocol and if we can somehow combine the signals so agents can signal you know okay i'm detecting quiescence but you gotta let me, decommit because i'm not ready here. um, briefly touch on some oth- some related work, um, a lot of work has been done in, a for task allocation and task oriented domains, here there aren't these um, they don't they don't have these test dependence networks they they have kind of they have tasks 
S1: but task oriented domains is not, that- that's a specific word that Rosenschein's Law ca- uses that's not 
S3: y- yes, that Rosenschein's Law can have defined and others such as Sandholm have also pursued work in that general area, domain, and the idea is that, to reallocate tasks among agents um, basically any reallocation of tasks is feasible but bec- but the- there are different costs depending on what combination of tasks that agents have. um, Anderson and Sandholm have looked at contract decommitment, and in in a task oriented type domain and they found, also that decommitment can greatly improve the efficiency, um Davis and Smith um, in- invented a protocol called Contract Net which actually does look at these hierarchical dependencies in the supply chain formation, um, it doesn't um, i- basically ta- does- it takes a different approach it does a top-down allocation starting from the consumer, um which means that if there are, um resource limitations in the system, it there would have to be some sort of backtracking to account for that and, um, u- usually you don't really u- to my knowledge that_ they're really they're they aren't rea- usually approach the problem of, of, of, strict resource limitations. they may look at different costs, depending on availability. and also, Sandholm and Baker have looked at some variants on that. um there's a wide variety of auction literature i've talked about the simultaneous ascending auctions, that there's there's a rich literature in that, to mention there um, var- 
S1: yeah i i wouldn't really say simultaneous. um, i wouldn't try to mention names on those cuz there's so much auction literature, [S3: okay ] to make an arbitrary choice but, (xx) 
S3: for any of the auction literature? 
S1: what? 
S3: for any of the auction literature? 
S1: yeah, for any of it. [S3: mkay ] you might, have (the sub-bullet) say simultaneous ascending, direct mechanisms combinatorial, mechanisms [S3: mkay. ] um, [S3: well, um ] but but you're not_ i mean i wouldn't try to say much about that i mean, i think just the i think the point that there's a lot of relevant, [S3: (there's a) ] auction literature it's not like you're really contributing to that. 
S3: right. yeah there's a lot of literature um, and um there are some approach- s- such as (general) (xx) auction combinatorial auctions which basically aggregate, um aggregate the decision maki- allocations for goods in one location, which can potentially, you know, give a much higher, um efficiency, sometimes optimal, but there are other trade-offs in in that, so. um, my research plan, um i want, i mentioned that i've only empirically established tha- the, um, that the s- about the solution conversions i'd like to actually prove that conjecture, um, i'm working with Jet Propulsion Laboratory to actually model and, um implement some of these, um, model and implement this system in the in a unmanned spacecraft domain. um, i'd like to evaluate the adductivity properties of the protocol i tal- i touched on, the problem of when mul- dif- new consumers come in and you know w- you know c- can we reallocate to meet the new value, um we can also look at problems where resources are lost and and i'd like to know, how how well the system responds to added value or reduced cost and and does it gracefully degrade or, 
S1: and by doing it in December ninety-nine you'll be just in time to, weather the Y-two-K 
S3: yeah 
<SS LAUGH> 
SU-M: that's right 
S3: and 
SU-M: (xx) adductivity properties in advance to that 
<SS LAUGH> 
S3: and, over the long term i'd also, really like to develop a model of an- an- model and analyze the strategic incentives for these various portions of the protocol. and um, two years from now i'd like to complete the thesis. and my contributions are i've, um by the time i'm done i will have a decentralized solution method, that combines a task allocation and scheduling, um and what's really new about this is it includes both the supply chain dependencies and strictly limited resources. also this quite- quiescence detection protocol, is is, to my knowledge is f- quite novel in the field of computational economics and it's very important for the imp- for to implement these, computational market systems and decentralize. 
S1: so i mean i don't disagree with that but i think, those two bullets are just really not equal, [S3: okay ] the first one is, much more significant than the second, [S3: okay ] but what, what i might suggest is just getting rid of the sub-bullets under the second and mayb- maybe add another... set of quo- set of, you know of things at that level, so, the main thing is you've got this decentralized solution method [S3: right right ] right? [S3: mhm ] and it's sort of on the side you've got quiescence detection, efficiency analysis, um, you know, activity properties, a- all those things that go with it [S3: mhm ] they're all sort of, there's equal things about that, but they're sort of enhance the the main show, which is, the the method itself. 
S3: mhm, so so (what) you're saying is, so add more bullets under this at this level? or, i'm i'm a little bit, (xx) 
S1: yeah actu- actually, 
S2: at the same level as quiescence...? 
S1: yeah, or maybe, group them under something else like, um, uh, analysis and, um, implementation. <P :05> so, (xx) 
S3: so this under analysis and implementation? 
S1: right. cuz quiescence i mean by by implementation i don't mean actually writing code but i mean, how to realize the protocol [S3: right right ] okay? quiescence detection, decommitment, you know all the other issues that you've raised, [S3: okay ] um, i wouldn't i wouldn't raise quiescence detection a- a- a- above those other ones and i, and, they really are all about, the first thing. 
S3: okay. 
S2: do you have any plans to, say anything about the computational cost of (the method?) 
S3: um, so the computational costs, um, i i wasn't planning on it i can say that, the bidding policies in the auctions, require nominal computation locally, be- the real time loss here is in tr- is communication. there there could be a lot of messages sent, depending on, [S2: and ] depending on a lot of factors um i do have a bound on the number, on the number of bids in the system, and we would expect that um so the, re- so the number of bids spec- really determines the com- the communication cost and, and so, 
S1: that's a good question to be prepared for. 
S2: and also the number, and, taking some, um, problem statement and converting it to your model, could be that the number of nodes explodes exponentially. 
S3: that's a little, um, [S2: i realize that it may not in other formulations ] if if we had agents that were potentially interested in any combination of goods yes, um we would have an exponential explosion. 
S1: actually yeah right, what is, the looking at the centralized solution what is complexity of this, problem. 
S3: well the- yeah this is, i i haven't proven this but i strongly believe it's this the problem is M-P complete to do centrally, because it very, closely resembles, a an- minimum and-or, it could be in a minimum and-or graph, certainly took 
S1: and is that is that known to be M-P complete? 
S3: yes, computing a minimum weight and-or, graph is M-P complete. this is a little bit different 
S1: it's restricted so you could (check) that might be worth knowing. 
S3: um yeah i haven't put the effort into, doing the, the translation um, certainly when i try and compute efficiency using, you know the A-star takes a long time 
<SS LAUGH> 
S2: right but if, [SU-M: yeah so ] i mean but yours could be doubly... 
S3: i doubt that. 
S1: well it shouldn't be better, but but [S2: right ] it's not obvious it should be, you know worse by any particular, you know 
S3: it looks a lot like a, minimum weight and-or graph problem... 
S7: um, i to re- to return to the the analogy with or the connection with the minimum weight an- and-or problem i mean that's, a computationally burdensome problem, which uh, one might want to parallelize if you have multiple processors you might wanna, exploit them and what you're presenting is a method for, parallelizing as well as decentralizing, the solution of a related problem is that interesting from a, i can imagine people in parallel computing (thinking that was really) interesting 
S3: i w- i would, i i would, be hesitant to argue that this is the b- that if you have all the information centrally i wouldn't be hesitant to argue that this is the best way to go about it. 
S1: even the best way to parallelize it? 
S3: well you have it all centrally and then you break it up, and parallelize it. 
SU-M: okay 
S4: yeah generally, when you parallelize an algorithm the best, not the best thing to do is like, have one processor in each node and only look at your, closest neighbor that's not the best (way) 
S1: right. um, since we've gone over um, quite a lot uh, probably should end it but thanks for all for your, patience and i think we've raised a bunch of things that, will come up again in time and of course, the committee's gonna raise just all sorts of, other, (considerably) comfortable things that, you can anticipate. but, i think you've got a lot to, sh- to defend yourself, i don't uh anticipate any difficulties 
S3: so i know we started late i f- can't remember when we started am i o- roughly okay on time here? 
S1: y- yes. 
S3: okay 
S1: but i think you'll need to monitor that, dynamically. because there's gonna be a l- you know res- shock events you know [S3: uhuh ] digressions and, you may need to f- think ahead of time about where you might, recover time if, if you fall behind. 
S2: you can skip stuff that you couldn't skip with us because they'll have read the paper, so 
S1: uh, that's that's a risky assumption 
<SS LAUGH> 
S2: well i mean, if you wanna if you need to make up time you might be able to say 
S1: so so alright they they are supposed to have read the paper, [S2: right ] so you can [S2: oh ] <SS LAUGH> you could you could say uh since you read it 
<SS LAUGH> 
S2: since you read it <LAUGH> i'll, i'll breathe thr- breeze through this section and, right 
SU-4: no they'll say oh, wait 
<SS LAUGH> 
S1: they, they usually will. um, yeah. okay? uh do uh, do we have any, topic for next week? i don't remember if we, set one... anybody want to set one? 
<P :05> 
SU-M: (xx) 
S1: it might be worth mentioning one of those points though one of those, you guys got several, things in your portfolio that, haven't been, talked about [SU-4: haven't talked about, okay, i'll do that. ] but yeah, let's figure out what it is, (xx) 
SU-4: you want us to m- can you meet, sometime today? 
S1: um... yeah. why don't we say... four-o'clock? 
SU-4: um, okay 
S1: i might be here earlier (though) 
SU-4: okay. but you have to, take off right now? 
S1: yeah 
S3: so so you said you'll be around? will you have any, time? 
S1: um, i got a proposal to get out this afternoon [S3: okay ] and i'm not sure, how long [S3: well i'll catch you on Monday ] that might (xx) alright. uh if i'm around this afternoon and i have slack i'll i'll try to (catch you) 
S2: i'll try to go fast 
S1: okay. um, okay. so we've got that set for next week. great. i think we're done. 
{END OF TRANSCRIPT}

