Variational convergence: Approximation and existence of equilibria in discontinuous games

Bagh, Adib

doi:10.1016/j.jet.2010.01.009

Cited by 20 publications

(14 citation statements)

References 32 publications

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“…Weak payoff security is weaker than generalized payoff security (gps) defined in Barelli and Soza [5], and generalized payoff security is weaker than payoff security (ps) defined in Reny [16]. Different combinations of these conditions imply different notions of better-reply security and the reader should consult Reny [16], Bagh and Jofre [3], and Barelli and Soza [5] for detailed treatments. In particular, Barelli and Soza [5] showed that a game satisfying weak reciprocal upper semicontinuity and generalized payoff security is generalized better-reply secure.The next result shows that, by further weakening generalized payoff security to weak payoff security, one obtains sequential better-reply security.…”

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%

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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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Section: Definition 7 (Bagh Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximation results for discontinuous games with an application to equilibrium refinement

Carbonell‐Nicolau

McLean

2012

Econ Theory

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“…First, jurisdictions that provide public funding often do so in form of a fixed, lump-sum payment. 2 Moreover, funds that are not spent during an election campaign may have few alternative uses. 3 Finally, a candidate's resources are also fixed if competition takes the form of pledges of political favors to voters, as the aggregate of such political favors may be exogenously given.…”

Section: Introductionmentioning

confidence: 99%

Sequential Majoritarian Blotto Games

Klumpp

Konrad

2018

SSRN Journal

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We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.

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“…Finally, the idea that limit points of approximate equilibria of the approximating game are themselves Nash equilibria of the original game is based on Bagh (2009), Carmona (2009 and Prokopovych (2010).…”

Section: Introductionmentioning

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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Variational convergence: Approximation and existence of equilibria in discontinuous games

Cited by 20 publications

References 32 publications

Approximation results for discontinuous games with an application to equilibrium refinement

Approximation results for discontinuous games with an application to equilibrium refinement

Sequential Majoritarian Blotto Games

Understanding some recent existence results for discontinuous games

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