Equilibrium Refinement for Infinite Normal-Form Games

Simon, Leo K.; Stinchcombe, Maxwell B.

doi:10.2307/2171776

Cited by 73 publications

(78 citation statements)

References 26 publications

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“…The work of Bagh [4] is closer to our approach. He introduces the notion of variational convergence for sequences of games and recovers approximation-based existence results of Dasgupta and Maskin [11], Simon [18], and Gatti [12]. We will provide a more detailed comparison between our work and that in [4] in Section 3 below.…”

Section: Introductionmentioning

confidence: 93%

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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: Introductionmentioning

confidence: 93%

“…Weak reciprocal upper semicontinuity is weaker than reciprocal upper semicontinuity (rusc) defined in Simon [18]. 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].…”

Section: Definition 7 (Bagh Andmentioning

confidence: 99%

Approximation results for discontinuous games with an application to equilibrium refinement

Carbonell‐Nicolau

McLean

2012

Econ Theory

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“…These existing approaches rely on the finiteness of action sets, and is thus not applicable to our setting. Simon and Stinchcombe (1995) proposed definitions of perfect equilibrium and proper equilibrium for infinite games with continuous strategy sets, however they did not propose any computational procedure for the resulting solution concepts. Exact computation of equilibrium refinements of continuous games such as MRMT sg remains a challenging open problem.…”

Section: Related Workmentioning

confidence: 99%

Protecting Moving Targets with Multiple Mobile Resources

Fang¹,

Jiang²,

Tambe³

2013

jair

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In recent years, Stackelberg Security Games have been successfully applied to solve resource allocation and scheduling problems in several security domains. However, previous work has mostly assumed that the targets are stationary relative to the defender and the attacker, leading to discrete game models with finite numbers of pure strategies. This paper in contrast focuses on protecting mobile targets that leads to a continuous set of strategies for the players. The problem is motivated by several real-world domains including protecting ferries with escort boats and protecting refugee supply lines. Our contributions include: (i) A new game model for multiple mobile defender resources and moving targets with a discretized strategy space for the defender and a continuous strategy space for the attacker.(ii) An efficient linear-programming-based solution that uses a compact representation for the defender's mixed strategy, while accurately modeling the attacker's continuous strategy using a novel sub-interval analysis method. (iii) Discussion and analysis of multiple heuristic methods for equilibrium refinement to improve robustness of defender's mixed strategy. (iv) Discussion of approaches to sample actual defender schedules from the defender's mixed strategy. (iv) Detailed experimental analysis of our algorithms in the ferry protection domain.

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“…a continuum extensive form game (see Simon and Stinchcombe [16]). We focus on Nash equilibria that satisfy sequential rationality, so that each player chooses actions optimally at any pro…le of supplier prices, p i .…”

Section: Private Contractsmentioning

confidence: 99%

“…In its absence, coordination failures can ensure that action pro…les which are not equilibria of G are equilibrium action outcomes of pvt -this is well known from the pricing of complements: More interestingly, this a¤ects mixed equilibria. Let us 1 Simon and Stinchcombe [16] develop equilibrium re…nements for in…nite normal form games, and argue for limit admissibility -equilibrium strategies should be limits of admissible strategies. In this extensive form example, limit admissibility and sequential rationality preclude existence.…”

Section: Private Contractsmentioning

confidence: 99%

Games played in a contracting environment

Bhaskar

2009

Games and Economic Behavior

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We analyze normal form games where a player has to pay a price to a supplier in order to play a speci…c action. Our focus is on supplier competition, arising from the fact that distinct suppliers supply di¤erent players, and possibly the di¤erent actions of the same player. With private contracts, where a player only observes the prices quoted by his own suppliers, the set of equilibrium distribution over player actions coincides with the set of equilibrium distribution when all actions are supplied competitively, at cost. With public contracts, the two distributions di¤er dramatically even in simple games.

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Equilibrium Refinement for Infinite Normal-Form Games

Cited by 73 publications

References 26 publications

Approximation results for discontinuous games with an application to equilibrium refinement

Approximation results for discontinuous games with an application to equilibrium refinement

Protecting Moving Targets with Multiple Mobile Resources

Games played in a contracting environment

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