Evolutionary Selection in Normal-Form Games

Ritzberger, Klaus; Weibull, Jörgen W.

doi:10.2307/2171774

Cited by 318 publications

(200 citation statements)

References 24 publications

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“…For instance, only a change of a single link is considered at a time, 8 but the 8 So, in a sense the notion of improving path looks at better-than reply rather than best reply dynamics. (See Ritzberger and Weibull [33] for a discussion of better-than reply dynamics.) definition is easily adapted to allow for the simultaneous addition or deletion of several links at a time.…”

Section: Improving Pathsmentioning

confidence: 99%

The Evolution of Social and Economic Networks

Jackson¹,

Watts²

2002

Journal of Economic Theory

834

755

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We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead to any given network at some time, where the stochastic process selects from among the statically stable networks and cycles. We apply these results to examples including the Gale-Shapley marriage problem. Thus the paper achieves two goals. First, it outlines a dynamic solution concept for networks. Second, it applies this concept to matching problems. Journal of Economic Literature Classification Numbers: A14, D20, J00. © 2002 Elsevier Science (USA)

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Section: Improving Pathsmentioning

confidence: 99%

The Evolution of Social and Economic Networks

Jackson¹,

Watts²

2002

Journal of Economic Theory

834

755

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“…From Ritzberger and Weibull (1995), Proposition 2, we know that a Nash equilibrium is asymptotically stable in the replicator dynamics if and only if it is strict. Hence we also know that all the eigenvalues of A at x have negative real part and we can consider the following scalar product in < N m :…”

Section: Proof Of Remarkmentioning

confidence: 99%

Learning strict Nash equilibria through reinforcement

Ianni

2014

Journal of Mathematical Economics

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This paper studies the analytical properties of the reinforcement learning model proposed in Erev and Roth (1998), also termed cumulative reinforcement learning in Laslier et al. (2001). The stochastic model of learning accounts for two main elements: the Law of E¤ect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially).The paper establishes a relation between the learning process and the underlying deterministic replicator equation. The main results show that if the solution trajectories of the latter converge su¢ ciently fast, then the probability that all the realizations of the learning process over a given spell of time, possibly in…nite, becomes arbitrarily close to one, from some time on. In particular, the paper shows that the property of fast convergence is always satis…ed in proximity of a strict Nash equilibrium.The results also provide an explicit estimate of the approximation error that could prove to be useful in empirical analysis.JEL: C72, C92, D83.

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“…2 Ritzberger and Weibull (1995) introduce the term behavior correspondence in a different context. Apart from technical issues (as e.g.…”

Section: Behavioral Rules and Correspondences And Tie-breakingmentioning

confidence: 99%

Robust stochastic stability

Alós–Ferrer

Netzer

2014

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 Revised Version January 2014Abstract A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.

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Evolutionary Selection in Normal-Form Games

Cited by 318 publications

References 24 publications

The Evolution of Social and Economic Networks

The Evolution of Social and Economic Networks

Learning strict Nash equilibria through reinforcement

Robust stochastic stability

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