A game with no Bayesian approximate equilibria

Hellman, Ziv

doi:10.1016/j.jet.2014.06.005

Cited by 19 publications

(31 citation statements)

References 7 publications

(11 reference statements)

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“…Purely atomic knowledge spaces were studied, as mentioned, in multiple works, for example, Simon (, ), Hellman (), Hellman and Levy (), Lehrer and Samet ().…”

Section: Bayesian Games With Purely Atomic Knowledge Spacesmentioning

confidence: 99%

“…In Bayesian games, Simon () presented an example of a three‐player Bayesian game over an uncountable state space that admits no measurable Bayesian equilibrium. This was further enhanced by an example in Hellman () of a two‐player Bayesian game that admits no measurable Bayesian ε ‐equilibrium for sufficiently small ε . More recently, Simon and Tomkowicz () have constructed an example of a three‐player Bayesian game that admits no measurable ex ante ε ‐equilibrium.…”

Section: Introductionmentioning

confidence: 99%

“… There is a relatively short step from the non‐existence of a measurable equilibrium to an example of a game without any equilibria at all, measurable or not. Details on this appear in Section 4 of Hellman (). …”

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confidence: 99%

“… Tracing out some of the cross‐inspirations: Simon and Tomkowicz () acknowledged ideas from Hellman (), which was inspired by studying Levy (), which in turn was inspired by Simon (). Hellman and Levy () followed the lead of an example in Lehrer and Samet (), which in turn was inspired by Simon (). …”

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confidence: 99%

“… Examples of non‐smooth type spaces can be found in Hellman (), Simon (), and Lehrer and Samet (); we do not present such examples here, as our focus is on smooth type spaces. …”

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confidence: 99%

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Measurable Selection for Purely Atomic Games

Hellman¹,

Levy

2019

ECTA

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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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“…Purely atomic knowledge spaces were studied, as mentioned, in multiple works, for example, Simon (, ), Hellman (), Hellman and Levy (), Lehrer and Samet ().…”

Section: Bayesian Games With Purely Atomic Knowledge Spacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“… Examples of non‐smooth type spaces can be found in Hellman (), Simon (), and Lehrer and Samet (); we do not present such examples here, as our focus is on smooth type spaces. …”

mentioning

confidence: 99%

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