Existence of equilibria in discontinuous Bayesian games

He, Wei; Yannelis, Nicholas C.

doi:10.1016/j.jet.2015.12.009

Cited by 29 publications

(22 citation statements)

References 19 publications

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“…In Balder and Rustichini [8], a further generalization to the case of uncountably many players is presented. In a recent paper, He and Yannelis [35] conduct an analysis similar to ours, based on the notion of disjoint payoff matching (cf. Allison and Lepore [2]), which is extended to the case of incomplete information.…”

Section: Related Literaturementioning

confidence: 99%

On the Existence of Nash Equilibrium in Bayesian Games

Carbonell‐Nicolau

McLean

2018

Mathematics of OR

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractWe furnish conditions on the primitives of a Bayesian game that guarantee the existence of a Bayes-Nash equilibrium. By allowing for payoff discontinuities in actions, we cover various applications that cannot be handled by extant results.

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Section: Related Literaturementioning

confidence: 99%

On the Existence of Nash Equilibrium in Bayesian Games

Carbonell‐Nicolau

McLean

2018

Mathematics of OR

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“…So far, the direct application of Reny’s theorem to incomplete-information contests has primarily been an expositional alternative. However, new results of practical relevance for contest theory might be feasible by combining arguments specific to contests with the insights of the more recent literature on equilibrium existence in discontinuous games (e.g., Carbonell-Nicolau and McLean 2017 ; He and Yannelis 2015 , 2016 ).…”

Section: Discussionmentioning

confidence: 99%

Unique equilibrium in contests with incomplete information

Ewerhart

Quartieri

2019

Econ Theory

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Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent. Keywords Imperfectly discriminating contests • Private information • Existence and uniqueness of equilibrium • Budget constraints • Rent dissipation JEL Classification C72 • D23 • D72 • D82 This paper was drafted while the second-named author was visiting the University of Zurich in spring 2013. Two anonymous reviewers and a Co-Editor provided extremely valuable comments. For useful discussions, we would like to thank

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“…In fact, BNE existence, albeit in behavioral and not necessarily pure strategies, will be established for much more general contests, where there may be no winner with positive probability, the probabilities of winning/costs need not be concave/convex in one's own e¤ort, and even a player who is the only one exerting positive e¤ort may lose (though with probability less than 1=2). It is important to note that, although the discontinuity of these contests is very mild, being con…ned to the zero-e¤ort pro…le, the recent results that guarantee BNE existence in discontinuous Bayesian games, of He and Yannelis (2016) and Carbonell-Nicolau and McLean (2018), can only be applied to contestsand we will show how -when the value of winning is common and there is always a winner. That is partially because most of the results require upper semi-continuity for every realization of players'types, the classical results of Milgrom and Weber (1986) and Balder (1988) guarantee BNE existence under quite mild conditions (such as compactness of action sets and absolutely continuous information).…”

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confidence: 90%

Bayesian Nash equilibrium existence in (almost continuous) contests

Haimanko

2021

Econ Theory

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We prove the existence of a behavioral-strategy Bayesian Nash equilibrium in contests where each contestant's probability to win is continuous in e¤orts outside the zero-e¤ort pro…le, monotone in his own e¤ort, and greater that 1=2 if that contestant is the only one exerting positive e¤ort. General type spaces, and in particular a continuum of information types, are allowed. As a corollary, the existence of a pure-strategy Bayesian Nash equilibrium is established in generalized Tullock contests, where the probability to win is strictly concave in one's own e¤ort.

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Existence of equilibria in discontinuous Bayesian games

Cited by 29 publications

References 19 publications

On the Existence of Nash Equilibrium in Bayesian Games

On the Existence of Nash Equilibrium in Bayesian Games

Unique equilibrium in contests with incomplete information

Bayesian Nash equilibrium existence in (almost continuous) contests

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