Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/122146
Authors: 
Xu, Zibo
Year of Publication: 
2013
Series/Report no.: 
SSE/EFI Working Paper Series in Economics and Finance 743
Abstract: 
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.
Subjects: 
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
JEL: 
C61
C62
C73
Document Type: 
Working Paper

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