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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.
Mechanism design in large games: Incentives and privacy. arXiv preprint arXiv:1207.4084,
, 2013
"... ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, ..."
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Cited by 20 (12 self)
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ABSTRACT We study the problem of implementing equilibria of complete information games in settings of incomplete information, and address this problem using "recommender mechanisms." A recommender mechanism is one that does not have the power to enforce outcomes or to force participation, rather it only has the power to suggestion outcomes on the basis of voluntary participation. We show that despite these restrictions, recommender mechanisms can implement equilibria of complete information games in settings of incomplete information under the condition that the game is largei.e. that there are a large number of players, and any player's action affects any other's payoff by at most a small amount. Our result follows from a novel application of differential privacy. We show that any algorithm that computes a correlated equilibrium of a complete information game while satisfying a variant of differential privacywhich we call joint differential privacycan be used as a recommender mechanism while satisfying our desired incentive properties. Our main technical result is an algorithm for computing a * We gratefully acknowledge the support of NSF Grant CCF1101389. We thank Nabil AlNajjar, Eduardo Azevdeo, Eric Budish, Tymofiy Mylovanov, Andy Postlewaite, Al Roth and Tim Roughgarden for helpful comments and discussions. correlated equilibrium of a large game while satisfying joint differential privacy. Although our recommender mechanisms are designed to satisfy gametheoretic properties, our solution ends up satisfying a strong privacy property as well. No group of players can learn "much" about the type of any player outside the group from the recommendations of the mechanism, even if these players collude in an arbitrary way. As such, our algorithm is able to implement equilibria of complete information games, without revealing information about the realized types.
On the value of correlation
 IN UAI05: PROCEEDINGS OF THE 21TH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 2005
"... Correlated equilibrium [1] generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents’ surplus (expected sum of payoffs) is greater than their surplus in all mixedstrategy equilibria. Following th ..."
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Cited by 18 (1 self)
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Correlated equilibrium [1] generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents’ surplus (expected sum of payoffs) is greater than their surplus in all mixedstrategy equilibria. Following the idea initiated by the price of anarchy literature [2, 3] this suggests the study of two major measures for the value of correlation in a game with nonnegative payoffs: 1. The ratio between the maximal surplus obtained in a correlated equilibrium to the maximal surplus obtained in a mixedstrategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal surplus to the maximal surplus obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games [4], a class of games that received a lot of attention in the recent literature.
Program equilibria and discounted computation time
 Center for
, 2008
"... Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite twoplayer game where each player can base their strategy on the other player’s strategies. Tennenholtz’s model allowed each player to produce a “loopfree ” computer program that had access to the code for both players. H ..."
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Cited by 9 (1 self)
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Tennenholtz (GEB 2004) developed Program Equilibrium to model play in a finite twoplayer game where each player can base their strategy on the other player’s strategies. Tennenholtz’s model allowed each player to produce a “loopfree ” computer program that had access to the code for both players. He showed a folk theorem where the result of any mixedstrategy individually rational play could be an equilibrium payoff in this model even in a oneshot game. Kalai et al. gave a general folk theorem for correlated play in a more generic commitment model. We develop a new model of program equilibrium using general computational models and discounting the payoffs based on the computation time used. We give an even more general folk theorem giving correlatedstrategy payoffs down to the pure minimax of each player. We also show the existence of equilibrium in other games not covered by the earlier work. 1
GameTheoretic Recommendations: Some Progress in an Uphill Battle
"... Game theory has become the central language for the analysis of multiagent systems. Moreover, the central gametheoretic solution concept, the Nash equilibrium, has become a standard tool for that analysis. A game is a general ..."
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Cited by 5 (0 self)
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Game theory has become the central language for the analysis of multiagent systems. Moreover, the central gametheoretic solution concept, the Nash equilibrium, has become a standard tool for that analysis. A game is a general
Noncooperative games with preplay negotiations
 CoRR
"... Abstract We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order to provide additional incentives for each other to ..."
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Cited by 4 (4 self)
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Abstract We consider an extension of strategic normal form games with a phase of negotiations before the actual play of the game, where players can make binding offers for transfer of utilities to other players after the play of the game, in order to provide additional incentives for each other to play designated strategies. The enforcement of such offers is conditional on the recipients playing the specified strategies and they effect transformations of the payoff matrix of the game by accordingly transferring payoffs between players. Players can exchange series of such offers in a preplay negotiation game in an extensive form. We introduce and analyze solution concepts for normal form games with such preplay offers under various assumptions for the preplay negotiation phase and obtain results for existence of efficient negotiation strategies of the players.
Privacy and truthful equilibrium selection for aggregative games
"... We study a very general class of games — multidimensional aggregative games — which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient w ..."
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Cited by 3 (2 self)
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We study a very general class of games — multidimensional aggregative games — which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large, we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator: a mechanism which has only the power to listen to reported types and provide nonbinding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an expost Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worstcase (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players n. We also apply our main results to a multidimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (expost Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games – previously, they were only known to exist in traffic routing games. We also give the first weak mediator that can implement an equilibrium optimizing a linear objective function, rather than implementing a possibly worstcase Nash equilibrium.
Implementation by Mediated Equilibrium
, 2007
"... Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals ’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the co ..."
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Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals ’ preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, a mediator coordinates the players’ strategies in a way that discourages deviation. Our main result is a complete characterization of social choice correspondences which are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important social choice correspondences which are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium.
Learning When to Take Advice: A Statistical Test for Achieving A Correlated Equilibrium
"... We study a multiagent learning problem where agents can either learn via repeated interactions, or can follow the advice of a mediator who suggests possible actions to take. We present an algorithm that each agent can use so that, with high probability, they can verify whether or not the mediator’s ..."
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We study a multiagent learning problem where agents can either learn via repeated interactions, or can follow the advice of a mediator who suggests possible actions to take. We present an algorithm that each agent can use so that, with high probability, they can verify whether or not the mediator’s advice is useful. In particular, if the mediator’s advice is useful then agents will reach a correlated equilibrium, but if the mediator’s advice is not useful, then agents are not harmed by using our test, and can fall back to their original learning algorithm. We then generalize our algorithm and show that in the limit it always correctly verifies the mediator’s advice. 1
Program Equilibrium in the Prisoner’s Dilemma via Löb’s Theorem
"... Applications of game theory often neglect that realworld agents normally have some amount of outofband information about each other. We consider the limiting case of a oneshot Prisoner’s Dilemma between algorithms with readaccess to one anothers ’ source code. Previous work has shown that coop ..."
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Applications of game theory often neglect that realworld agents normally have some amount of outofband information about each other. We consider the limiting case of a oneshot Prisoner’s Dilemma between algorithms with readaccess to one anothers ’ source code. Previous work has shown that cooperation is possible at a Nash equilibrium in this setting, but existing constructions require interacting agents to be identical or nearidentical. We show that a natural class of agents are able to achieve mutual cooperation at Nash equilibrium without any prior coordination of this sort. 1