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Implementing Mediators with Cheap Talk

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Abstract

In this work we study the effects of cheap-talk in games with rational agents. We begin by showing that all asynchronous interactions between n players and a mediator can be t-bisimulated without the mediator if n>4t. Intuitively, t-bisimulation means that for any deviation performed by an adversary controlling at most t players in the scenario with the mediator or in the scenario without the mediator there exists an equivalent deviation in the other scenario (i.e., a deviation that produces the same outcome). We then use this result to show that any (k,t)-robust strategy in a game with n players and a mediator in an asynchronous system can be implemented with cheap talk if n>4k+4t. A (k,t)-robust strategy is one in which no coalition of t malicious players can decrease the payoff of anyone else and no coalition of k players can increase their payoff even in coalition with the t malicious players. We also prove that the result above can be satisfied if n>3k+4t whenever honest players can punish players that are caught deviating. A similar result can be shown for synchronous systems, but in this case we only require that n>2k+3t. We also show that for every protocol π for n players and all k<n there exists a belief system that is consistent with π in which all coalitions K of at most k players believe that, if there is any deviation during the execution of the protocol, then it was someone sending an \emph{incorrect} message to a player in K. We call these beliefs k-paranoid. Intuitively, k-paranoid beliefs are such that all coalitions of size at most K believe that the remaining players are being honest between them. We use these beliefs to extend the results regarding (k,t)-robustness by showing that all k-resilient sequential equilibria with a mediator can be implemented with cheap-talk if n>4k in asynchronous systems or n>3k in synchronous systems. We finish this work by proving a matching lower bound for most of our results.

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202 pages

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Date Issued

2021-08

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Keywords

Cheap Talk; Coalitions; Distributed Computing; Game Theory; Mediators

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Union Local

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Committee Chair

Halpern, Joe

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Committee Member

Pass, Rafael N.
Tardos, Eva

Degree Discipline

Mathematics

Degree Name

Ph. D., Mathematics

Degree Level

Doctor of Philosophy

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Government Document

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Attribution 4.0 International

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dissertation or thesis

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