The Existence of Equilibrium in Discontinuous Economic Games, I: Theory

Maskin, Eric; Dasgupta, Partha

doi:10.2307/2297588

Cited by 880 publications

(548 citation statements)

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“…Existence of an equilibrium is guaranteed by theorem 5 of Dasgupta & Maskin [1986]. By lowering its price a firm always benefits from an increase in demand (this property is not influenced by our rationing rule), its payoff is therefore left lower semicontinuous (l.s.c.)…”

mentioning

confidence: 93%

Bertrand competition and Cournot outcomes: further results

Boccard¹,

Wauthy

2000

Economics Letters

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mentioning

confidence: 93%

Bertrand competition and Cournot outcomes: further results

Boccard¹,

Wauthy

2000

Economics Letters

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“…Carmona [10] provides another variation on the theme of better-reply security. Before stating it formally, we need the following definition.…”

Section: Definition 7 (Bagh Andmentioning

confidence: 99%

“…If each X i is a subset of a vector space, the following Unlike better-reply security of Reny [16], generalized better-reply security of Barelli and Soza [5], and weak better-reply security of Carmona [10], our notion of sequential better-reply security does not ensure the existence of Nash equilibria in compact, quasiconcave games. In fact, the example of Section 3.3 in Carmona [9] is a compact, quasiconcave game satisfying weak reciprocal upper semicontinuity and weak payoff security (hence sequential better-reply security) for which no Nash equilibria exist.…”

Section: Definition 7 (Bagh Andmentioning

confidence: 99%

“…Sequential better-reply security is weaker than Barelli and Soza's [5] generalized better-reply security, which is, in turn, weaker than the notion of better-reply security introduced in Reny's [16] seminal work. Sequential better-reply security is implied by weak reciprocal upper semicontinuity (Bagh and Jofre [3]) and weak payoff security (Dasgupta and Maskin [11]), and is weaker than weak better-reply security, as defined in Carmona [10]. Moreover, Barelli and Soza's [5] generalized Bsecurity and McLennan et al's [15] B-security need not imply Statement C.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…The crucial point is that we cannot even guarantee the existence of a mixed strategy equilibrium. The main existence theorems for games with discontinuous payoffs given by Dasgupta and Maskin (1986), Simon (1987) and the recent one by Reny (1999) can be applied only in the case of finitely many firms.…”

Section: The Modelmentioning

confidence: 99%