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Xu, Zibo
Year of Publication: 
Series/Report no.: 
SSE/EFI Working Paper Series in Economics and Finance 743
We consider a basic stochastic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. Following Young's papers, we call a state stochastically stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. We prove that, for all finite extensive-form games of perfect information, the best-reply dynamic converges to a Nash equilibrium almost surely. Moreover, only Nash equilibria can be stochastically stable. We present a 'centipede-trust game', where we prove that both the backward induction equilibrium component and the Pareto-dominant equilibrium component are stochastically stable, even when the populations increase to infinity. For finite extensive-form games of perfect information, we give a sufficient condition for stochastic stability of the set of non-backward-induction equilibria, and show how much extra payoff is needed to turn an equilibrium stochastically stable.
evolutionary game theory
Markovs chains
equilibrium selection
stochastic stability
games in extensive form
games of perfect information
backward induction equilibrium
Nash equilibrium components
best-reply dynamics
Document Type: 
Working Paper

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