The Politics of Negotiating as a Group with Peter Buisseret | a16z crypto Research Series

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delighted to introduce Peter Buser who is visiting us from the government department at Harvard University. Peter, please take it away. >> Fantastic. Thank you very much. It's been a wonderful week. Uh and thank you for the opportunity to present this applied theory work with my co-author Vincent Anessie who is at the University of Luxembourg. So what are we going to do in this paper? We're going to ask how is it that groups negotiate? Okay, how do groups negotiate? And you might say why would you do such a thing? Well, we believe that in real world bargaining, at least in a lot of real world bargaining, at least one of the negotiating parties is typically a group. That is to say, an aggregation of some individuals or or subgroups. So think about coalitions of labor unions, trade associations, lobbies that are

composed of multiple firms, international alliances, countries where executives have to have their you know their treaties with other countries uh ratified by legislatures and of course a prototypical example for our context would be Dows which by construction are kind of programmatically managed uh groups consisting of possibly many many uh individuals. And so the motivation for trying to open up uh the question of group negotiations is how internal frictions might impact uh the group's external negotiations. So let me give you a quick sense of the key elements of our theory and then motivate it with some some examples. So we're going to have a group uh of more than one member that is going to repeatedly negotiate

with an external party which we're going to call the agent. The group members are going to have properties that to some extent would have to be present in any theory of groups. One is that they share some commonality. They're united by a common purpose which in our framework is going to be extracting surplus from the counterparty. They all agree that all else equal, they would like to get more collectively, but they're going to hold some idiosyncratic preferences. And in our framework, it's going to be different valuations from reaching an agreement. And those features combined with uncertainty about a characteristic of the counterparty with whom they negotiate which we're going to call the agents resolve. It'll be the modeled as

a cost of making a concession is going to create some disagreement amongst group members about the kinds of offers that they would like the group to make. So what would be a Dow based motivation for this? Well, DAO stakeholder interest as we know vary tremendously along a number of dimensions. their economic stakes, large or small token holders, their ideology, okay? Are they concerned with profit or are they focused more on, you know, decentralization and community sovereignty? They may also be distinguished by their roles and they frequently negotiate with third parties. You know, classic example would be a regulator. And you can imagine that the regulator would have some private information about its enforcement priorities, its resources, uh thresholds for pursuing legal remedies, desire to

make a particular case, uh a kind of leading case that sets the tone for future interactions. It could also be other entities like for example a centralized exchange uh which may have private information about its liquidity needs and its regulatory risks. And in these kinds of situations, the DAO will have to collectively make a decision between what you might call a dovish approach in which you make concessions that kind of guarantee legal or regulatory compliance uh versus taking a harder line that ensures the the kind of supremacy of decentralization and sovereignty. So a recent example, a kind of prominent example of this was uh bybit and Paris swap now uh velour. So in February uh of this year, the Lazarus

group, which is purportedly a North Korean kind of cyber attacking group, uh famously purportedly hacked Sony in 2014, you may remember uh they hacked by bit to the tune of about $1.5 billion and laundered funds through a number of exchanges including Paris swap. So inadvertently Paris swap ended up uh making transaction fees to the tune of about $100,000 off of this uh laundered money. So bybit uh posted an onchain governance proposal which essentially said please freeze those proceeds and give them back to us and this triggered a lot of uh uh viciferous debate all of which I read uh in which you know the various participants in the DAO sort of coalesed into three groups those who are

in favor of a full refund okay so these would be the ones who were afraid of legal or regulatory risk were not too sure about being seen to benefit from the proceeds of crime those who said Let's make some concession, but let's not be too generous. In particular, let's refund them 90% but keep a 10% bug bounty, which is in fact in keeping with BBIT's own uh rules. And then there were the hardliners who said, "Give them nothing back. Code is law." And so, you know, a smattering of the discussions. One user betraying his or her propensity for compromise called hardcore said, you know, service has been delivered. It's a real pity this happened, but it's not our fault. There's a little bit of a culture clash because bybit is centralized and so uh you know Austian

is saying you know should we be back stops for C5 failures uh it undermines the whole idea and then other users who who said we should just do this uh it would be good and there was a lot of uncertainty on the chat uh about the legal obligations that the uh exchange would have and the potential for lawsuits. An interesting feature which is not pertinent to today's talk by the way is that many of the members agreed that they should uh facilitate an automatic distribution of revenue to commit the DAO not to being in a position where these funds could be frozen and then subject to a negotiation externally. Um so that's just an interesting aside about the commitment power of uh uh of the blockchain. The outcome, in case you're interested, was uh they modified the proposal to a 90%

rebate and it was passed on a margin that makes Brexit look like a landslide. So 49.56% in favor, 49.54 against. And you know, the trauma of it led to a renaming and uh and so that was the outcome of that vote. So we think these are these are situations we should be interested in studying. >> And so that was that was pure tokenbased voting, >> I believe. So yes, >> and that was binding. >> Yes. Exactly. Exactly. Um, so let me give you some highlights from our theory. Oh, yeah. Dan, >> do we know that was the participation rate high or or or low?

>> I don't I don't recall, but we could Yeah, we could find out. I don't I don't recall. There was abstension, but I don't Yeah, I don't remember the the the amount exactly. So, let me just give you some highlights from the theory before we sort of dive in. So, one of the highlights from our our framework, we're going to have a notion of collective choice. A big part of the the issue of our of our framework is going to be the aggregation of preferences within the group uh in its external environment. And we're going to find that uh small shifts in power amongst group members will have direct effects. If you give more power to people who are more intrinsically kind of hostile to agreement or have a lower value from agreement, that's going to have a direct effect on the group's uh negotiating

position. It will also have indirect effects because it will change how others behave in anticipation of those and those shifts in power can be very much stronger the indirect forces than those that are direct. They can sometimes counterveail and go in the opposite direction. And so uh one implication of this is that if you make even small changes to the way in which you have uh uh voting or delegation mechanisms, group behavior expost may be very sensitive and change in ways that are much larger um than the perceived changes in voting rules. Another thing we're going to talk about is delegation.

Uh so we're going to come back to a topic that was raised a lot on on Monday in in Manon's talk. Delegation in our framework can be a tool for creating alignment between uh members of the DAO. In particular, we tend to think of delegation as something that I do to members with whom I agree or I would agree if I had the same information as them. And in political science, they call that the ally principle. You delegate to players who are like you. We're going to have uh instances in which that principle fails and in which I would like to delegate to members whose interests are different from my own because that serves as a commitment to behavior in the future that changes other members behavior in ways that I like. And so one implication of that is that systems that facilitate transparent

delegation meaning everyone can see where the distribution of power is. Okay, delegation is not private. um it can help Dowo members to achieve consensus and in some limited cases it can be a substitute for side payments that can achieve a notion of a group optimal choice. So we're not going to have side payments in this setting but there is going to be a limited extent to which the transfer of power can be a partial substitute. Before I get to the the theory, let me just highlight that the general topic of how groups decide is a research frontier to which uh people in this audience have directly contributed and all of them are asking some broader version of the question how do internal frictions uh impact a group's interaction with an external

environment. Okay. So for example, auctions. So uh Barani, Gardian, Ruff Garden, that's a setting in which you have biders uh who can be groups and so the group has to somehow have an aggregation rule that takes individual bids and turns them into a collective bid. There has to be a rule that tells you how an item or items that are won are distributed amongst members. And you may want uh a property like for example incentive compatibility to bid your your valuation. And it turns out it can be very difficult to achieve that in ways that preserve for example efficiency efficient allocation of goods. And the paper explores that. Um in the field of disclosure you can have information providers who are groups. Think about a collection of firms giving uh making a

representation to a congressional committee. Different members of the lobbying group might value certain information being released that others would not like. And then there's a related work to our own by Kim Palfrey and Zidell uh which looks at what's called crisis bargaining which is quite close to our framework. But there's is a setting in which there is no exanti conflict amongst group members. They have a common preference and expectation but there are perturbations um uh once once play begins. So it's they're pursuing a similar question but in a in a somewhat different different way than ours. So let me get to our framework.

So, we're going to have a group of members, which I call n, and they're going to repeatedly negotiate with a privately informed agent. So, in each of a finite number t of periods, the group is going to make a demand to the agent in exchange for some kind of concession. And the agent is going to observe the demand and say yes, I will concede, which we're going to call taking the action one, or no, I will not concede, which is taking the action zero. So an example from from the real world might be don't have a nuclear program uh and in exchange we will hand you some kind of package of uh uh concessions like we will unfreeze a bunch of assets that we've been holding uh or don't sue us and in exchange here is the amount of funds that we're going to return uh from

our from our uh uh swaps. I want to highlight in some phrase our framework is deliberately naive. It builds right on top of a seminal uh paper by Hart and Troll from 1988. And so if you're interested, that version is one in which the group is a single member. So that's the one the one uh variation that we want to pursue. We want to see how far we can get. Okay, busiest slide. So member I is going to have a stage payoff which will take the value zero if the agent doesn't concede. So you should think of this as the net benefit to the agent conceding for a member. So if a takes the value one, I'll get my indiv individual value, okay, from uh an agreement having been reached. Okay, so this is going to be an

individual I specific term and I'm going to pay whatever cost uh we offered in exchange for the concession and I'm going to order the members according to their commonly known benefits. Okay, so all the private information is on the side of the agents cost. The members are going to share a common discount factor delta. And the agent stage payoff again is zero if she makes uh no concession. If she concedes, she gets the concession that the group offered minus a cost of concession C. And we're going to assume that C is a privately observed characteristic of the agent. Her cost from conceding. You can think of it as her resolve. In my example with the regulator, it could be, you know, how much would I like to go

after this particular firm or entity. Okay. So, if I'm very prone to pursue uh uh you know, litigation, that's like having a high cost of concession. We'll assume that C can take two values for now. Um it can either be low or high and the group will have a common prior P that the agent's cost of concession is low. We're going to take for today a kind of extreme view of the commonality of the group members objective. We're going to assume that even the most kind of pessimistic or lowest benefit group member could find it efficient to trade even with the high cost of resolve agent. Okay. So we'll do all of our analysis today on that and if we have time at the end I'll tell you about what happens if there are some group members

who if they learned that the agent had a sufficiently high cost would no longer want to trade. Okay. And the agent will have a discount factor delta zero. Everyone will maximize average discounted payoffs. So collected choice for today is going to take a very simple form. At the start of each period, there's going to be a distribution over group members in which member I is going to be selected with probability pi. It could be zero. Okay, it could be one. The selected member will simply choose the group sufferer. Okay, so condition on being recognized, you're effectively a dictator. And so we're going to call pi the collective choice rule. And pi is going to summarize all of the uncertainty that group members have about who in the future will be

empowered to make decisions. This is a very very reduced form kind of collective choice rule. And in the paper we look at much richer varants with proposals and amendments little bit like the by bit example. And we look at voting rules that can that that can be very broad. But this is this is all that we need to get our forces out. Is it crucial for your results that a pi be stationary over time? >> Is it crucial? No, it is not. So, in a previous version of the paper, we allowed the group members to uh also change the decision rule in each period.

um in this variant as long as so if there were an exogenous if there were a distribution over distributions for example at least as far as this example which is all I'm prepared to say on the top of my head our results would extend yeah good good no it's a very it's a very good >> so this is not a group decision bas there's a random person that makes the decision >> that is a version of collective choice that's like uh you know a random dictatorship but again what I want to emphasize the thing that I want to uh that I need or that we need for these for our you know our model to have bite is that you're not totally sure whether someone who agrees with your negotiating position is going to be in charge tomorrow. One way in which that can arise very starkly is if I have a chance

of being recognized to make the decision and you and I are going to disagree. Another one might be you get to be the one who votes but I get to choose the proposal and so I can use my choice of proposal to steer the second period period offer in a way that perhaps is not the one you would choose if you were getting to make the proposal. So there are lots of more subtle ways in which you can do this and but that's really what we need. >> You're basically reducing it to a singleton every round in some sense like I get to choose and then we play a single game. >> Yeah. Exactly. So effectively. Exactly. Exactly. And this again is just the core element of the framework which is why we can do much richer stuff is all that we need is that group members aren't sure

that the person in charge tomorrow will be someone who would make the offer they would have wished to make. Exactly. No. Very good. Very good. >> Peter, can I ask a question? >> Andy. Yeah. >> Remote majoritarianism. So like the crab idea that uh you can't commit to anything other than majority rule. >> So so in in Congress the idea would be like Congress could in principle adopt a rule like this but then expost if the median member of Congress observes that the person chosen to decide disagrees with them. They can't commit not to just on the fly have another vote that says undo this. Mhm.

>> And so it does that matter here that is there are you assuming some kind of commitment to the to the particular rule? >> Yes. So certainly pi is considered immutable for the purposes of this example. Uh I suppose you know if you had something like uh let me think if you had majority rule I guess as long as there was still some uncertainty about who gets to make proposals and there's a status quo on the table then there could still be some uncertainty about what offers will be submitted to a vote and thus what offers for example a medium voter will get to choose between in the future and that would be enough for us. that if uh there's no uncertainty about who's going to be uh in charge tomorrow, a lot of

the interesting action in our model is going to reduce because then it it more or less will be as if there is a singleton group member. Yeah. Good. Very good. Okay. Great. Okay. Little bit of housekeeping. So, we're going to look at pure strategy perfect equilibria and we're going to resolve indifference uh by assuming that if you're indifferent between multiple offers, you choose the highest. We're going to impose a parameter restriction. Those of you who are in this literature will be familiar with the ratchet effect. And I'll come back to this later on. But, uh, it's a parameter condition that was given to us, you know, nearly 40 years ago. Uh, if it's violated, if the agent is too forward-looking, they're not going to be willing to reveal information about their cost of concession today, no matter how generous the group is, and a

lot of our interesting action will fall flat. And I I'll come back to that later on. And the final concession for expediency is that I'm going to have a two period setting today. So this is going to be kind of the box of chocolates version of the talk. No formal statements of theorems, mainly a bunch of examples. Okay, quick word on terminology before we leap into the analysis. So I'm going to assert that in each of my two periods uh on the equilibrium path, my group, in particular recognized member is going to choose from one of two possible offers. What is called a pooling offer in the sense that it's an offer that the group anticipates both a high and low resolve agent would accept. So in particular observing that the offer is accepted is not going to tell the group anything

about the agents type. Hence it pulls the types together. And a second offer called a separating offer which the group is going to calibrate such that only the low resolve type would have accepted. And thus if I see that the uh offer is accepted I'm going to learn that the agent has low cost and if I see it's rejected I'm going to infer that she has high cost. Okay. So separating offers allow the group to learn. Uh pooling offers do not. And so for the purposes of our application, think about the separating offer as being tantamount to a more aggressive negotiation strategy because it raises the risk that the group will fail to strike an agreement if they make an offer that is then rejected by a high-cost agent.

>> And just making sure in terms of information, the only thing we don't know is the type of the agent. >> Exactly. We only have So >> everything else we know. >> Yeah. Exactly. So, you know, literally in this case, it's like we we go to the Dow, we go to the Paris swap board and we see, you know, we know what Hardcore thinks. We know what Alian thinks. Um, and so their bees can be can be can be learned uh directly by observation. We could in this example accommodate a little bit of private information about types. Uh, but beyond the the example, it would be it would be very difficult. Settings with two-sided private information is notoriously messy. Okay, good. So, let's do some backwards induction. So, let's start in the second period. And on the path, there are two things that could have happened. Okay,

that got us into the start of this period. It could be that we made a separating offer in the first period that allowed us to learn the agent's type because the agent accepted it and revealed she was low cost or she rejected it and revealed she was high cost. At that point, every group member agrees on what we should do. We should make an offer that leaves whatever type of agent we believe we're facing indifferent between accepting or rejecting. And so if I learned that the agent's cost is C, whoever is recognized is just going to propose C. Remember, this is a consequence of a presumption that even the lowest benefit member has a benefit that is higher than the cost that they would have to give the agent to compensate her for agreeing. The other possibility is that the group made a pooling offer in the

first period and we learned nothing. Okay? And so we retain the prior belief. And this is where there's potentially some difference of opinion about what we should do. So if I'm member I, if I want to screen the agent, I should offer exactly the transfer that would leave the lowcost type indifferent between accepting and rejecting. And because this is the end of the interaction, there's no future play. I should just offer her CL. And so with probability P, the agent will accept and I'll get my benefit minus the concession. I could Oh, yeah. Question from >> you assume that the agent is myopic.

>> No, no, no. I'm not assuming the agent is myopic. This is the fine. This is the terminal period. So remember terminal one. >> Yes. Exactly. Exactly. No, the agent is for it's very important that the agent is Yeah. is farsighted. Yeah. Exactly. >> At least internalizes the future to some degree. So this is the last period. >> I'm I'm asking because of the first point. It could be that they falsely learned that the agent's cost is CL because the agent agreed. So they could be that for so this is why I'm being a little bit I'm trying to let me say let me put it as a let me put it like this on the equilibrium path an offer will either reveal that the agent's cost is low or the agent will accept and the group will

believe that the agent rejects and the group will believe with probability one that the agent's cost is high. Now that belief may be incorrect because the agent rejected and of course what offer was made in the first period to induce the lowcost type to accept is a part of the analysis that will deter exactly lowc cost types. Yeah, exactly. The alternative to making a screening offer that risks rejection with probability one minus P is to make a pooling offer which simply means offering CH in which case I know that I'm going to get the agent to make the concession but I'm going to have to pay the higher cost.

And unsurprisingly, this is going to give us a threshold on benefits B star below which I want to make the separating offer and above which I'd like to make the pooling offer. And that allows us to write down an equilibrium probability that the group screens in period 2 conditional or not having screened in the first period. And I'm going to call that lambda 2. And it's just the sum of the probability of all the members whose benefits BI are below B star being recognized. And to make life interesting, I'm going to assume that the pi is such that this lambda 2 is interior. Okay, so there's some genuine uncertainty about what would happen after an initial pooling offer.

Okay, so let's go back to the first period. So this is going to go exactly to you and I's question about what are the paths that might have got us to the second period. So in the first period, if I'm recognized to be the proposer, I again face a choice between two possible offers. a separating offer that will reveal the agent's cost but possibly forego trade today or a pooling offer that I know will be accepted but will not reveal any useful information going into the second period. Okay. And what incentives do I have to give the load type to kind of out herself? The challenge is that if I'm a load type and I reveal my cost today, I'm going to be exploited tomorrow. This is the classic ratchet effect. This is not a novel contribution of our paper, but it's going to give us the incentive

constraint that must be satisfied by the first period offer, namely the concession minus the cost of making that concession. So what the group gives me minus my cost of concession plus a continuation value of zero because tomorrow I'm going to be held to my participation constraint has got to be at least as good as rejecting the offer convincing the group mistakenly that I'm a high type and thus securing a more generous concession tomorrow than I would be entitled to if they knew my type. Okay. And that's going to give us an XL. And in the dynamic model, this thing is going to take place over many many many future periods. And that's why if this thing uh is too big, we're never

going to be able to find offers that the group members are willing to make. And that's why we had the parameter restriction earlier on that limits delta zero. The alternative is a pooling offer. This one is a bit more straightforward. even in the first period in this in you know if I offer you a uh you know a high a high uh offer today if you accept it uh tomorrow you're going to get nothing okay because tomorrow regardless of what offers the group makes it's never going to make an offer that's more generous than ch and so either you're going to get an offer you reject or you get an offer that's going to leave you indifferent and that's true regardless of whether you accept or reject so the high type is going to get uh no rent the low cost type is going to be given some

additional incentive to reveal her type. This is then going to allow us to write down continuation values for the group members. So if I make the separating offer, I run the risk of failing to reach an agreement today. But there is a value of learning which is that I guarantee we'll have an agreement tomorrow and that agreement will be calibrated in terms of the offer we make tomorrow to the agents cost. If I learned that you're a lowcost type, you know, then I'm going to make you that offer. And that's going to be with probability P because that's the fundamental. And if I learned that you're a high cost uh of concession type, then you know, I forgo trade today, but at least I get it right uh in the future. And there's a continuation value from pooling. And what you what I want you to see is that while the value

of separation doesn't depend on the voting rule or the collective choice, it doesn't depend on collective choice because once we've learned the agents type, we have commonality of preference. So we all would do the same thing. But if we make the pooling offer, we leave some political risk on the table because I don't know whether tomorrow's proposer is going to be one who wants to pull with probability 1 minus lambda 2 or screen with probability lambda 2. And so there's a chance that I'm going to be misaligned with the person who's making the decision tomorrow. And by leaving uncertainty on the table, I've created scope for disagreement in the future.

And that's going to be the key mechanism of our incentives. There was a hand up. Yeah, I was wondering uh if the group made a pulling offer and the agent accepts, we're still going to go to the next round of the game. >> Yeah. So, the question is, I guess, does the interaction conclude whenever an offer is accepted? No. The answer is the con the interaction takes place over the entire horizon. And if the agent uh accepts for example a separating offer then I'm going to learn that the agent is uh a lowcost type and my offer is in all my offers in the future are going to be calibrated to that type but we're going to continue to engage and if it's a high cost type sorry if I make a pooling offer in the agent uh which the agent will accept then in all subsequent

periods we're going to face a calculation that looks like this again. >> Okay. But you did say t equals two. >> Yes. So in the two- period model, if I make a pooling offer, we go into the next period and we face this calculation. >> That's the end of the game. >> That will be the end of the game. Exactly. But t could be large in uh in the full setting. Exactly. Okay, good. So the question then arises, when do I prefer the separating versus the pooling offer in our in our extended environment? And it turns out that there is a threshold as you might expect a threshold benefits type such that if I'm below that threshold I want to screen and if I'm above it I want to pull. What I want to emphasize is that that threshold beta 1 can be written as a

function of the equilibrium probability of screening in period 2. So changes in my beliefs about who is going to be the decisive group member tomorrow are going to have a direct impact on my incentives to make a more aggressive or less aggressive offer today. So what does it look like? If delta is bigger than delta zero, the group is more prone to screen. Okay, the intuition is screening conveys a common benefit to all members of the group which is it reveals the agent's type allowing the group to calibrate its offer better in the subsequent period and that's something they all like. But you also have to hand the agent compensation for that. The group benefits the future at rate delta, the agent at delta zero. And so the net of these two things is going to tell you

whether the group is getting a net surplus from screening or whether it's forking it over to the to the agent. So in this example, in the first period, uh members 1, two, and three would want to screen. Member four would want to pull. In the second period, member 3's preference is then to pull. Members one and two want to keep screening. Okay? So the preference over screening and pooling reflects the period and we can do the same thing when delta is less than delta 0. So then the question becomes well how do my beliefs about lambda 2 which is tantamount to saying changes in the collective choice rule impact where this threshold is and of course one thing we could do is just take a derivative but to try and get some intuition for the forces I'm going to do an example. So how do conflicts

among group members shape their preferred negotiating position? The answer, as I tried to foreshadow, is that in this setting, all of their conflicts are driven exclusively by uncertainty about the agents willingness to concede. Okay. In practice, of course, there are other conflicts which we can bolt on, but uh but this this turns out to be enough for us to say some interesting things. So the more uncertainty we have about the group uh sorry about the agent the more scope there is for different members of the group to disagree over how to trade off the value of surplus extraction from the risk of not getting a deal. So separating offers reduce disagreement amongst group members because they reduce their uncertainty about the agents type. So even in a model where

you have a single group member there is a value of learning okay that is really built into these models by construction the group setting augments that benefit because learning is a form of conflict management within the group as well okay so to get a sense of of of how that works and the governance implications I described earlier let me just give you a toy example so let's suppose we have a group of two members and as I've written it member two would like to pull in both periods okay because B2 is above the first period threshold and the second period threshold. Member one would like to screen in both periods. So they disagree. And let's suppose initially that uh pi 1 is zero so that member two is a dictator. That means we're going to make the pooling offer in both periods.

What happens if a little bit of proposal power is handed over to member one? Okay. So if we take pi 1 from zero to some epsilon. Well, there's a direct effect which is that the probability of screening at least in the second period is going to go from zero up to epsilon. But of course, that's going to have indirect effects on member two's preference in the first period. In particular, member two is now scared that after an initial pooling offer, member one is going to impose an aggressive screening offer that is too aggressive from member two's perspective. That's going to lower two's continuation value from pooling the agents type. Okay? And in principle, it could change her preferred period offer, period one offer from pooling to

screening. So member two's anticipation that member one has become more powerful changes member two from favoring pooling to favoring screening. And so the probability of screening shifts from zero to one. Okay. So group behavior changes in a very sharp way even though the distribution of political power within the group has changed by only a small amount. >> So it's kind of a power of a credible threat. >> Yes. Exactly. And it's a credible threat from member 2's perspective through this exactly through exactly this channel exactly. So it's an indirect effect. So this is a world in which you know the indirect effect augments the direct effect uh in magnitude but they both go in the same direction. So one might then ask well is that always the case. Uh and it turns out that the answer is no.

Okay. So I can imagine a world in which delta is less than delta 0. So imagine that the agent is quite patient uh relative to the group. In my example here, member one is a dictator. So pi 1 is equal to one. And as I've written it, member one would like to pull in the first period because her benefit is above the threshold in period one. But it's below bar star. So she would then switch to screening in the second period. What happens to the probability of screening if I take a little bit of power away from member one and give it to the higher benefit member two? An intuition might be, well, the probability of screening must go down as a result. Okay, I mean it can't because uh you know it's currently zero, but it it it surely will not go up. Why might

that not be true? Well, member one now worries that after an initial pooling offer, member two is going to make too generous a pooling offer in the second period. This lowers member one's value from making uh you know a friendly offer in the first period and it could change her preferred period one offer from pooling to screening. Okay, not not guaranteed, but you can construct examples in which that's true. And so in this case the probability of screening increases from zero to one minus epsilon even though we only shifted power from a low uh benefit member to a high one. So the indirect effect uh reverses the direct effect in magnitude and in sign.

So what are the takeaways? >> A quick question. So you assume your common knowledge of benefits level right? >> Yes. Exactly. So um say that they only had Beijian priors over each other's benefits. Do you do you know whether >> Yeah. So at least still continue similarly >> we haven't we I think a full you know an analysis in the extended model is with the with the finite horizon we haven't done >> but one way in which you can sort of see that um those for our forces are still there is that it's effectively creating some uncertainty about lambda 2 and so if I believe that power is shifting to people whose benefits lie above or below the threshold bar star if it's shifting

within then it's not going to have any impact um but But if it's shifting in ways that potentially misalign me with other members, then we're going to have the same sort of forces playing out. Um, exactly. So I at least in this setting we could have some uncertainty and again with only two types of agent, you know, once you screen benefit uncertainty becomes becomes mood. Um, so so there's some aspects of this example that are very generous to making it making it work. Exactly. Okay. So relative to the single member setting and this is a result we can state formally in the paper. relative to a world in which I were a dictator. So my pi were equal to one. Any other collected choice rule gives me a weekly incent a weekly greater incentive to make a screening

offer in every period. Okay. And the uh you know we we can talk about the argument but regardless of primitives if I fear losing power in the future to someone who misalign with me they only misalign with me when we're uncertain about the agents type. that reduces my benefit to maintaining that uncertainty with generous offers that both types of agent would accept and that increases my net benefit from screening to try and do conflict management. So a feature of this model is that more information always creates agreement and we can talk about whether that is a more you know robust general property uh or or whether it's you know uh there are settings in which the opposite would be true but in this setting uh learning creates agreement and as I said power shifts

have direct and indirect effects sometimes they intensify these direct forces and sometimes they can uh even reverse them okay so let's talk briefly about delegation so the idea we wanted to explore is members may be willing to give up proposal power or more generally their political power in order to align the interests of other members with their own. So we consider in the paper a notion of admissible power transfers and actually we we it's part of a set of conditions that Jackson and Winsky elaborated in a paper on networks in in in the late 90s and I'll just describe it informally a bilateral exchange of power. So if I take some of my pie and I give it to Tim it has to be the case that I'm strictly better off from doing it and Tim can be no worse off from receiving it. Okay, so that's the that's

the idea and we look at uh starting from an initial pi, what are the sorts of power transfers uh that would satisfy this notion of admissibility and then we ask well who would stand to benefit from changes in power and how would they impact the group's negotiating strategy as summarized by its probability of screening. So here's an example three members and let's uh assume that the pies and the primitives are such that member three would want to pull in the first period and indeed in the second period. So member one is the only PR member who would want to screen in the second period. And let's suppose that every member is realized with positive probability. Could member two benefit from delegating to member one? You can show that member two would never benefit

from delegating to member three or vice versa. What really matters is delegation on either side of threshold B star because that's what's going to change behavior in the second in the second period and thus influence first period screening incentives. So suppose that member two hands her PI 2 over to member one says I'm going to delegate to you. That's going to increase the probability of screening in the second period because member two is now out of the game in the second period. So member one is now more likely to be realized and that actually would hurt member two conditional on reaching the second period and having residual uncertainty about the agents type. However, it also scares member three because member three now anticipates uh that there's going to be screening in the second period that

lowers her value from pooling the agent possibly encouraging her to screen in the first period and thus giving to her preferred outcome. Okay. So that's the sense in which delegation provides a form of commitment and you know it wouldn't work for member two to delegate to someone uh who doesn't want to screen in the second period which is what she doesn't want to do. She has to delegate in this case to someone who misaligns with her. And so what we show in the paper more generally is that whenever uh the group is patient relative to the agent which is sort of implied by the group being sufficiently patient given that we already assume that delta 0 can't be too high. It always must be the case that the chain of delegation is from a higher to a lower benefit member.

And in a precise sense that we make precise in the paper, it's going to speed up screening. So it's going to kind of hasten. It's going to lead to a more aggressive strategy. In the opposite case, anything goes. Delegation can be from higher to lower. It can also be uh from lower to higher benefit members and it can either speed up or slow down screening. So the impacts on negotiation are ambiguous. Which of these two does a common delta uh go to? >> Yes. So with a common delta uh with with all of the linearity in this in the payoffs, the group surplus from extraction is exactly offset by the agent surplus. And so the threshold B star is going to be the same in every single period. So it's just a it's not a terribly interesting setting from our

perspective. Yeah. No, it's a good question. So what else do we do in the paper? So we characterize the unique equilibrium modulo our refinement to pure strategies and you know what we end up with is a sequence of thresholds which are kind of recursively derived. Each threshold is a function of the equilibrium probability of screening in every subsequent period conditional or not having screened today. And we do some comparative statics on the thresholds that are very similar to what I showed you. And we also allow some group members to have benefits that are sufficiently low that if they learned that the agent uh is a high-cost type, they would not want to participate anymore. And the short uh punchline is the value of screening is not very high if you're a high benefit person trying

to win these guys over because they're never going to be willing to make uh high offers anyway. And so there's nothing really you can teach them that they don't already know about what they would want to do. And so the net effect is that uh any transfer of power to these guys say uh from member four is just going to uh kind of reduce the value of screening as an information tool and so it's going to slow down this learning process. So it's going to lead to less aggressive offers. Okay. And then we look at much richer collective choice processes. Uh we we have a non-ooperative model with proposals and amendments and voting rules. Uh and we recover very similar forces to the one that I described here. When you say unique equilibrium, is this uh sequential or perfect basian?

>> It's perfect Beijing with the no signal in the sense of there's a no signaling what you don't know requirement built on top. Yeah, exactly. >> Is there any situation where not not uncovering information actually helps the negoti negotiation? Like in this case like learning the type is actually helping the negotiation. Um but maybe when the C for instance when the assumption on the B1 and CH is flipped um would that be an example? >> Yeah. So in in this setting it's you know this the um it it's in it's a kind of weaker version of that which is learning cannot create agreement but it will not actively create disagreement because those lowbenefit members they already disagree with high benefit

members and there's no there's no amount of learning. But I think you're right that in even though in our setting more information creates agreement. I think that there is a lot of uh there are a lot of examples in which the more we learn the more we can disagree. You know an example would be we learn from an initial round of negotiations that one of the members most preferred options is just no longer available to them. Uh and that then makes them less willing to contribute to say the other members project or something like that. So that's not something that we recover in this model. I think the next step would be to ask when does more information create agreement and when does more information create disagreement and how might someone want to take advantage of that to try and uh you know stop decisions from being made or something

like that. So I I agree that's exactly the right path we think to go down. Thank you.