Deterministic Equilibrium Selection Under Payoff-Perturbed Dynamics
39 Pages Posted: 6 Jul 2014
Date Written: May 16, 2014
Abstract
This paper studies models of population game dynamics where players make stochastic choices because of payoff perturbations. The goal is to obtain deterministic equilibrium selection, where the action distribution in the population globally converges to Nash equilibria with probability 1 in a finite time, under a moderate level of payoff perturbations. Exploiting the tractable nature of bounded perturbations, we characterize almost-sure global stability in a finite population setting by generalizing risk-dominance in many action games. We also characterize conditions for (approximate) global asymptotic stability under a continuum population setting allowing unbounded perturbations; this leads to a stronger conclusion that waiting times are uniformly bounded in the population size.
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