Stochastic stability in finite extensive-form games of perfect information

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SSE/EFI Working Paper Series in Economics and Finance ; No. 743

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Existence and Stability Conditions of Equilibrium ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
• Subject: 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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Xu, Zibo
• Event: Veröffentlichung
• (who): Stockholm School of Economics, The Economic Research Institute (EFI)
• (where): Stockholm
• (when): 2013

Further information

• Handle: http://hdl.handle.net/10419/122146
• Last update: 10.03.2025, 11:46 AM CET