Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment

Bagh, Adib; Jofré, Alejandro

doi:10.1111/j.1468-0262.2006.00724.x

Cited by 50 publications

(31 citation statements)

References 6 publications

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“…This weakening of upper semicontinuity is analogous to that of reciprocal upper semicontinuity obtained through weak reciprocal upper semicontinuity, since the latter allows all players' payoffs to jump down provided that some player can compensate such a fall somewhere in his action space. Thus, our existence result is better regarded as a generalization of the existence result of Dasgupta and Maskin [3] in the same spirit of the generalization of Reny's Corollary 3.3 obtained by Bagh and Jofre [1].…”

Section: Introductionsupporting

confidence: 66%

“…This condition, which we name weak upper semicontinuity, strengthens the notion of weak reciprocal upper semicontinuity of Bagh and Jofre [1]. This is accomplished by imposing a similar requirement as theirs, although not on the players' payoff function but rather on an extended payoff function that allows each player to deviate singly.…”

Section: Introductionmentioning

confidence: 89%

“…This is accomplished by imposing a similar requirement as theirs, although not on the players' payoff function but rather on an extended payoff function that allows each player to deviate singly. 1 Our existence result then states that a compact, quasiconcave game has a Nash equilibrium provided that it is weakly upper semicontinuous and weakly payoff secure.…”

Section: Introductionmentioning

confidence: 94%

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An existence result for discontinuous games

Carmona

2009

Journal of Economic Theory

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We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin [3] and that it is neither implied nor does it imply the existence theorems of Baye, Tian, and Zhou [2] and Reny [5]. Furthermore, we show that an equilibrium may fail to exist when, while maintaining weak payoff security, weak upper semicontinuity is weakened to reciprocal upper semicontinuity. Journal of Economic Literature Classification Numbers: C72

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Section: Introductionsupporting

confidence: 66%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 94%

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An existence result for discontinuous games

Carmona

2009

Journal of Economic Theory

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“…Several authors have studied perfect equilibria in games with infinitely many actions (e.g., Simon and Stinchcombe [19], Al-Najjar [2], Carbonell-Nicolau [6,7,8] [17] notion of perfection to games with infinitely many actions including their concept of limit-of-finite (lof ) perfect equilibrium. An lof perfect equilibrium is defined as the limit of -perfect equilibria for successively finer finite approximations to an infinite game.…”

Section: Application To Perfect Equilibriummentioning

confidence: 99%

Approximation results for discontinuous games with an application to equilibrium refinement

Carbonell‐Nicolau

McLean

2012

Econ Theory

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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 August 2011 AbstractWe provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed, and compare these conditions to those considered in the related literature. We then prove existence results for a new "finitistic" infinite-game generalization of Selten's [17] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification.

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“…This result is then used to obtain the existence result of Carmona (2009) and a new existence result based on the ideas of Radzik (1991), Ziad (1997 and Carmona (2010). Part of the characterization relies on the notion of weak upper semicontinuity introduced by Bagh and Jofre (2006). A game G = (X i , u i ) i∈N is weakly reciprocal upper semicontinuous if for all (x, α) in the frontier of the graph of…”

Section: Analogously To Lemma 4 We Have Thatmentioning

confidence: 99%

Understanding some recent existence results for discontinuous games

Carmona

2010

Econ Theory

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We introduce a new condition, weak better-reply security, and show that every compact, locally convex, metric, quasiconcave and weakly better-reply secure game has a Nash equilibrium. This result is established using simple generalizations of classical ideas. Furthermore, we show that, when players' action spaces are metric and locally convex, it implies the existence results of Reny (1999) and Carmona (2009) and that it is equivalent to a recent result of Barelli and Soza (2009). Our general existence result also implies a new existence result for weakly upper reciprocally semicontinuous and weakly payoff secure games that satisfy a strong quasiconcavity property.

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Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment

Cited by 50 publications

References 6 publications

An existence result for discontinuous games

An existence result for discontinuous games

Approximation results for discontinuous games with an application to equilibrium refinement

Understanding some recent existence results for discontinuous games

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