Potential Games with Continuous Player Sets

Sandholm, William H.

doi:10.1006/jeth.2000.2696

Cited by 366 publications

(324 citation statements)

References 22 publications

Supporting

Mentioning

321

Contrasting

Unclassified

Order By: Relevance

“…Thus, games with continuous strategy spaces involve random matching with a continuum of types. Examples can be found in Sandholm (2001), Oechssler and Riedel (2002), Hofbauer et al (2008). In these games, the distribution of strategies in the population is given by a probability distribution on the strategy space S, written as τ.…”

Section: Examplesmentioning

confidence: 99%

“…Moreover, for a wide class of random matching models with a continuum population, it is not possible to capture the relevant attributes of all the agents in a finite type space. This is the case, e.g., for the models described in Cavalcanti and Puzzello (2010), Green and Zhou (2002), Lagos and Wright (2005), Molico (2006), Shi (1997), Zhu (2005), where there are no upper bounds on money holdings or money holdings are perfectly divisible, or those described in Hofbauer et al (2008), Oechssler and Riedel (2002), Sandholm (2001), van Veelen and Spreij (2009), where infinite strategy sets matter.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Independent random matching

Podczeck

Puzzello

2010

Econ Theory

View full text Add to dashboard Cite

Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the sense that certain desirable properties are satisfied for any assignment of types to agents. The result applies to infinitely many types of agents, thus covering random matching models which are currently used in the literature without a foundation. Furthermore, the paper provides conditions guaranteeing uniqueness of random matching. JEL classification: C00, C02, C73, C78Keywords: Random matching; Involution; Independence; Continuum population; Fubini extension * We thank an anonymous referee for valuable comments and for suggestions on how to improve the presentation of the material of this paper.

show abstract

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Independent random matching

Podczeck

Puzzello

2010

Econ Theory

View full text Add to dashboard Cite

show abstract

“…Hofbauer and Sandholm (2009) consider the evolution of aggregate behavior in a class of population games called contractive games (or stable games), a class which includes zero-sum games, games with an interior ESS, and concave potential games (Sandholm (2001)) as special cases. They define population dynamics in terms of choice functions called revision protocols, which describe the rates at which agents switch between actions.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Interpretations of Integrability for Game Dynamics

Sandholm

2013

Dyn Games Appl

Self Cite

View full text Add to dashboard Cite

In models of evolution and learning in games, a variety of proofs of convergence rely on the assumption that the players' choice functions are integrable. This assumption does not have an obvious game-theoretic interpretation. We address this question by introducing probability models defined in terms of piecewise smooth closed curves through R n ; these curves describe cycles in the performances of the available actions. We establish that a choice function is integrable if and only if in the probability model induced by each such curve, the rate at which players switch to a randomly drawn action is uncorrelated with a certain binary signal. The binary signal specifies whether the performance of the randomly drawn action is improving or worsening, and can also be interpreted as a signal about the performances of actions other than the one randomly drawn.

show abstract

“…Skyrms [31], Swinkels [32], Weibull [34], Berger and Hofbauer [1,2], Hofbauer [20], Meertens et al [22] and Sandholm [26,27,28]). In honor of its three inventors it has been named Brown-von Neumann-Nash dynamics (BNN).…”

Section: Introductionmentioning

confidence: 99%

“…For the case of human strategic interaction this seems too restrictive. In contrast, the BNN dynamics satisfy the property of "inventiveness" (Weibull [34]), or equivalently, "noncomplacency" (Sandholm [26]). Namely, if there are any (used or unused) strategies that (would) perform better than the current population average, at least one of them must increase in frequency.…”

Section: Introductionmentioning

confidence: 99%

Brown–von Neumann–Nash dynamics: The continuous strategy case

Hofbauer

Oechssler

Riedel

2009

Games and Economic Behavior

View full text Add to dashboard Cite

In John Nash's proofs for the existence of (Nash) equilibria based on Brouwer's theorem, an iteration mapping is used. A continuoustime analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown-von Neumann-Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify sufficient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory.Journal of Economic Literature Classification Numbers: C70, 72.

show abstract

Potential Games with Continuous Player Sets

Cited by 366 publications

References 22 publications

Independent random matching

Independent random matching

Probabilistic Interpretations of Integrability for Game Dynamics

Brown–von Neumann–Nash dynamics: The continuous strategy case

Contact Info

Product

Resources

About