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46
Robust game theory
, 2006
"... We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides ..."
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Cited by 55 (0 self)
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We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides an alternative distributionfree equilibrium concept, which we call “robustoptimization equilibrium, ” to that of the ex post equilibrium. We prove that the robustoptimization equilibria of an incompleteinformation game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robustoptimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results.
Beyond Equilibrium: Predicting Human Behaviour in Normal Form
, 2010
"... It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies. However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players ’ actual behaviour. In this study, we consider a wide range of widelystudied models ..."
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Cited by 41 (4 self)
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It is standard in multiagent settings to assume that agents will adopt Nash equilibrium strategies. However, studies in experimental economics demonstrate that Nash equilibrium is a poor description of human players ’ actual behaviour. In this study, we consider a wide range of widelystudied models from behavioural game theory. For what we believe is the first time, we evaluate each of these models in a metaanalysis, taking as our data set largescale and publiclyavailable experimental data from the literature. We then propose a modified model that we believe is more suitable for practical prediction of human behaviour. ii Table of Contents Abstract................................... ii
Resource selection games with unknown number of players
, 2006
"... In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the c ..."
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Cited by 40 (10 self)
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In the context of preBayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safetylevel equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the common ignorance about the number of players. In order to perform the analysis we define safetylevel equilibrium for preBayesian games, and prove that it exists in a compactcontinuousconcave setup; in particular it exists in a finite setup. 1
Iterated Regret Minimization: A New Solution Concept
"... For some wellknown games, such as the Traveler’s Dilemma or the Centipede Game, traditional gametheoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, which ex ..."
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Cited by 27 (2 self)
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For some wellknown games, such as the Traveler’s Dilemma or the Centipede Game, traditional gametheoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, which exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler’s Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition. As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret. 1
Mediators in Position Auctions ∗
, 2008
"... A mediator is a reliable entity which plays on behalf of the players who give her the right of play. The mediator is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator cannot enforce behavior; that is, agents can play in the game directly with ..."
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Cited by 21 (5 self)
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A mediator is a reliable entity which plays on behalf of the players who give her the right of play. The mediator is guaranteed to behave in a prespecified way based on messages received from the agents. However, a mediator cannot enforce behavior; that is, agents can play in the game directly without the mediator’s help. A mediator generates a new game for the players, the mediated game. The outcome in the original game of an equilibrium in the mediated game is called a mediated equilibrium. Monderer and Tennenholtz introduced a theory of mediators for games with complete information. We extend the theory of mediators to games with incomplete information, and use the new theory to study position auctions, a central topic in practical and theoretical electronic commerce. We provide a minimal set of conditions on position auctions, which is sufficient to guarantee that the VCG outcome function is a mediated equilibrium in these auctions.
Minimax regret and strategic uncertainty
, 2008
"... This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and s ..."
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Cited by 13 (1 self)
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This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a nondegenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).
Mechanism Design with Partial Revelation
, 2008
"... With the emergence of the Internet as a global structure for communication and interaction, many business to consumer and business to business applications have migrated online, thus increasing the need for software agents that can act on behalf of people, institutions or companies with private and ..."
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Cited by 10 (6 self)
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With the emergence of the Internet as a global structure for communication and interaction, many business to consumer and business to business applications have migrated online, thus increasing the need for software agents that can act on behalf of people, institutions or companies with private and often conflicting interests. The design of such agents, and the protocols (i.e., mechanisms) through which they interact, has therefore naturally become an important research theme. Classical mechanism design techniques from the economics literature do not account for the costs entailed with the full revelation of preferences that they require. The aim of this thesis is to investigate how to design mechanisms that only require the revelation of partial preference information and are applicable in any mechanism design context. We call this partial revelation mechanism design. Reducing revelation costs is thus our main concern. With only partial revelation, the designer has some remaining uncertainty over the agents types, even after the mechanism has been executed. Thus, in general, the outcome chosen will not be optimal with respect to the designers objective function. This alone raises interesting questions about which (part of the) information should be elicited in order to minimize the degree of suboptimality
Characterizing Solution Concepts in Games Using KnowledgeBased Programs
"... We show how solution concepts in games such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of knowledgebased programs. Intuitively, all solution concepts are implementations of two knowledgebased programs, one a ..."
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Cited by 8 (3 self)
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We show how solution concepts in games such as Nash equilibrium, correlated equilibrium, rationalizability, and sequential equilibrium can be given a uniform definition in terms of knowledgebased programs. Intuitively, all solution concepts are implementations of two knowledgebased programs, one appropriate for games represented in normal form, the other for games represented in extensive form. These knowledgebased programs can be viewed as embodying rationality. The representation works even if (a) information sets do not capture an agent’s knowledge, (b) uncertainty is not represented by probability, or (c) the underlying game is not common knowledge. 1
Mechanism Design with SetTheoretic Beliefs
 Proceedings of the IEEE 52nd Annual Symposium on Foundations of Computer Science 2011 (FOCS
, 2011
"... In settings of incomplete information, we put forward (1) a very conservative —indeed, purely settheoretic — model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of ra ..."
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Cited by 8 (5 self)
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In settings of incomplete information, we put forward (1) a very conservative —indeed, purely settheoretic — model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs. We exemplify the applicability of our new approach for singlegood auctions. In particular we show that, under our solution concept, there exists a simple normalform mechanism, which always sells the good, always has nonnegative revenue, and guarantees (up to an arbitrarily small, additive constant) a revenue benchmark that is always greater than or equal to the secondhighest valuation, and sometimes much greater. By contrast, we also prove that the same benchmark cannot even be approximated within any positive factor, under classical solution concepts. ∗An earlier version of this work has been presented at the Symposium on Foundations of Computer Science, 2011. The present version is under review at the Journal of Economic Theory (special issue dedicated to the interface between economics and computer science). We would like to thank Gabriel Carroll, Robert Kleinberg, and Ronald Rivest for discussions that motivated us to prove results stronger than the ones we originally had. We also would like to thank Amos Fiat and Anna Karlin for helping us improve the presentation of our results. Many thanks also to Andrés Perea for helping us understand beliefs in economic settings, to Paul Milgrom for helping us clarify the fragility of implementation at equilibria, and to Elchanan BenPorath, Sergiu Hart, and Philip Reny for helping us clarify our connections to expost equilibria. (Any remaining lack of clarity is solely due to us!) This work is supported in part by ONR Grant No. N000140910597. 1