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Imitation dynamics with payoff shocks

Panayotis Mertikopoulos 1, 2 Yannick Viossat 3
1 MESCAL - Middleware efficiently scalable
LIG - Laboratoire d'Informatique de Grenoble, Inria Grenoble - Rhône-Alpes
2 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
Abstract : We investigate the impact of payoff shocks on the evolution of large populations of myopic players that employ simple strategy revision pro-tocols such as the "imitation of success". In the noiseless case, this process is governed by the standard (deterministic) replicator dynamics; in the presence of noise however, the induced stochastic dynamics are different from previous versions of the stochastic replicator dynamics (such as the aggregate-shocks model of Fudenberg and Harris, 1992). In this context, we show that strict equilibria are always stochastically asymptotically stable, irrespective of the magnitude of the shocks; on the other hand, in the high-noise regime, non-equilibrium states may also become stochastically asymptotically stable and dominated strategies may survive in perpetuity (they become extinct if the noise is low). Such behavior is eliminated if players are less myopic and revise their strategies based on their cumulative payoffs. In this case, we obtain a sec-ond order stochastic dynamical system whose attracting states coincide with the game's strict equilibria and where dominated strategies become extinct (a.s.), no matter the noise level.
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Submitted on : Tuesday, January 6, 2015 - 2:45:55 PM
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Panayotis Mertikopoulos, Yannick Viossat. Imitation dynamics with payoff shocks. International Journal of Game Theory, Springer Verlag, 2016, 45 (1-2), pp.291-320. ⟨10.1007/s00182-015-0505-7⟩. ⟨hal-01099014⟩



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