On the Existence of Nash Equilibrium in Bayesian Games

Abstract

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.

Robust Mechanisms Under Common Valuation

“…Notice that if S is a finite or countably infinite set, or if the signals are independent according to , then the information structure is automatically product continuous. Theorem 1 of Carbonell‐Nicolau and McLean () implies that under any product continuous information structure, an equilibrium exists in the exponential price auction.…”

On the existence of approximate equilibria and sharing rule solutions in discontinuous games

“…Recently, it has been extended to discontinuous payoffs under a uniform payoff security assumption (e.g., Carbonell-Nicolau and McLean 2015), with application to auctions.…”

Essays in economic theory

“…This assumption is widely adopted in the setting of Bayesian games; see, for example, Milgrom and Weber (1985), Balder (1988), Jackson et al (2002), Loeb and Sun (2006) and Carbonell-Nicolau and McLean (2015). Notice that the (AC) assumption is imposed even when the payoff function is continuous in the action variables.…”

“…By Theorem 11, the game G 0 is payoff secure. Then applying Lemma 3 in Carbonell-Nicolau and McLean (2015), the mapping…”

“…Remark 29. By extending the uniform payoff security condition of Monteiro and Page (2007) and adopting the (AC) assumption, Carbonell-Nicolau and McLean (2015) proved the existence of behavioral/distributional-strategy equilibria in Bayesian games with discontinuous payoffs. In particular, they showed that the ex ante game G 0 is payoff secure when the Bayesian game G satisfies their uniform payoff security condition.…”