Bayesian games with a continuum of states

Hellman, Ziv; Levy, Yehuda John

doi:10.3982/te1544

Cited by 12 publications

(22 citation statements)

References 31 publications

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“…We also argue that this is more or less all we can hope for. It is known from earlier results by, among others, Simon (2003) and Hellman and Levy (2013), that beyond the restriction of countable type spaces, BNE-and hence also perfect BNE-may not exist.…”

Section: Existencementioning

confidence: 96%

“…Such a Bayesian game admits a BNE, in view of part (I) of Theorem 1 in Hellman and Levy (2013). In the next theorem we show that such a Bayesian game even admits a perfect BNE.…”

Section: Existencementioning

confidence: 96%

“…2 non-existence It is difficult to obtain existence results beyond the above conditions. This is highlighted by part (II) of Theorem 1 in Hellman and Levy (2013), who provide examples of Bayesian games in which players have type spaces with the cardinality of the continuum without a BNE. We also refer to Simon (2003) for Bayesian games without BNE.…”

Section: Existencementioning

confidence: 97%

“…Such rather abstract type spaces are not unusual, see for instanceSimon (2003) orHellman and Levy (2013), and the references therein.…”

mentioning

confidence: 98%

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Behavioral perfect equilibrium in Bayesian games

Bajoori

Flesch

Vermeulen

2016

Games and Economic Behavior

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JEL classification: C72Keywords: Trembling hand perfect equilibrium Bayesian game with infinite type spaces Behavior strategy Second-price auction with incomplete information We develop the notion of perfect Bayesian Nash Equilibrium-perfect BNE-in general Bayesian games. We test perfect BNE against the criteria laid out by Kohlberg and Mertens (1986). We show that, for a focal class of Bayesian games, perfect BNE exists. Moreover, when payoffs are continuous, perfect BNE is limit undominated for almost every type. We illustrate the use of perfect BNE in the context of a second-price auction with interdependent values. Perfect BNE selects the unique pure strategy equilibrium in continuous strategies that separates types. Moreover, when valuations become independent, the equilibrium converges to the classical truthful dominant strategy equilibrium. We also show that less intuitive equilibria in which types are pooled are ruled out by our selection criterion. We further argue that standard selection criteria for second-price auctions have no bite here. Bidders have no dominant strategies, and the separating equilibrium is not sincere.

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Section: Existencementioning

confidence: 96%

“…Such a Bayesian game admits a BNE, in view of part (I) of Theorem 1 in Hellman and Levy (2013). In the next theorem we show that such a Bayesian game even admits a perfect BNE.…”

Section: Existencementioning

confidence: 96%

Section: Existencementioning

confidence: 97%

“…Such rather abstract type spaces are not unusual, see for instanceSimon (2003) orHellman and Levy (2013), and the references therein.…”

mentioning

confidence: 98%

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Behavioral perfect equilibrium in Bayesian games

Bajoori

Flesch

Vermeulen

2016

Games and Economic Behavior

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“…Lehrer and Samet () presented an example of a knowledge space, based on an example in Simon (), over which there is a measurable common prior yet over each individual common knowledge component no common prior exists. Hellman and Levy () contains a similar knowledge space in which, in each common knowledge component, players can find an acceptable bet (or trade) to which they agree, but, over the entire space, the players must agree to disagree as there exists no measurable mutually agreeable bet.…”

Section: Introductionmentioning

confidence: 99%

Measurable Selection for Purely Atomic Games

Hellman¹,

Levy

2019

ECTA

Self Cite

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A general selection theorem is presented constructing a measurable mapping from a state space to a parameter space under the assumption that the state space can be decomposed as a collection of countable equivalence classes under a smooth equivalence relation. It is then shown how this selection theorem can be used as a general purpose tool for proving the existence of measurable equilibria in broad classes of several branches of games when an appropriate smoothness condition holds, including Bayesian games with atomic knowledge spaces, stochastic games with countable orbits, and graphical games of countable degree—examples of a subclass of games with uncountable state spaces that we term purely atomic games. Applications to repeated games with symmetric incomplete information and acceptable bets are also presented.

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Language Games

Asher

Shrivastava

2016

Logical Aspects of Computational Linguistics. Celebrating 20 Years of LACL (1996–2016)

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In this paper we summarize concepts from earlier work and demonstrate how infinite sequential games can be used to model strategic conversations. Such a model allows one to reason about the structure and complexity of various kinds of winning goals that conversationalists might have. We show how to use tools from topology, set-theory and logic to express such goals. Our contribution in this paper is to offer a detailed examination of an example in which a player 'defeats himself' by going inconsistent, and to introduce a simple yet revealing way of talking about unawareness. We then demonstrate how we can use ideas from epistemic game theory to define various solution concepts and justify rationality assumptions underlying a conversation.

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Bayesian games with a continuum of states

Cited by 12 publications

References 31 publications

Behavioral perfect equilibrium in Bayesian games

Behavioral perfect equilibrium in Bayesian games

Measurable Selection for Purely Atomic Games

Language Games

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