2014/12/25 by Panayotis Mertikopoulos, Yannick Viossat, Mertikopoulos, Panayotis +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #Dynamical Systems (math.DS) #Evolutionary Game Theory and Cooperation #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #Probability (math.PR)
paper · doi:10.48550/arxiv.1412.7842
openalex publication_date 2014/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the impact of payoff shocks on the evolution of large populations of myopic players that employ simple strategy revision protocols 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 second 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.