Stochastic stability of replicator dynamics with random jumps

Asymptotic stochastic stability;evolutionarily stable strategy;invariant measure;Lyapunov function;Nash equilibrium;recurrence;stochastic differential equation

Vlasic, Andrew

关键词: Asymptotic stochastic stability;    evolutionarily stable strategy;    invariant measure;    Lyapunov function;    Nash equilibrium;    recurrence;    stochastic differential equation;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/34446/Vlasic_Andrew.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. Inparticular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects onthe fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able toestimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.