The Annals of Applied Probability

The emergence of rational behavior in the presence of stochastic perturbations

Panayotis Mertikopoulos and Aris L. Moustakas

Full-text: Open access

Abstract

We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game’s payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the “aggregate shocks” approach of evolutionary game theory. Irrespective of the perturbations’ magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game’s strict Nash equilibria are stochastically asymptotically stable. We complement our analysis by illustrating these results in the case of congestion games.

Article information

Source
Ann. Appl. Probab., Volume 20, Number 4 (2010), 1359-1388.

Dates
First available in Project Euclid: 20 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1279638789

Digital Object Identifier
doi:10.1214/09-AAP651

Mathematical Reviews number (MathSciNet)
MR2676942

Zentralblatt MATH identifier
1195.91011

Subjects
Primary: 91A26: Rationality, learning 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 91A22: Evolutionary games 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Asymptotic stochastic stability congestion games dominance exponential learning Lyapunov function Nash equilibrium replicator dynamics stochastic differential equation

Citation

Mertikopoulos, Panayotis; Moustakas, Aris L. The emergence of rational behavior in the presence of stochastic perturbations. Ann. Appl. Probab. 20 (2010), no. 4, 1359--1388. doi:10.1214/09-AAP651. https://projecteuclid.org/euclid.aoap/1279638789


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