Open AccessSampling best response dynamics and deterministic equilibrium selection
Author(s) -
Oyama Daisuke,
Sandholm William H.,
Tercieux Olivier
Publication year - 2015
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te1405
Subject(s) - iterated function , mathematics , equilibrium selection , stability (learning theory) , selection (genetic algorithm) , mathematical economics , distribution (mathematics) , stability theory , sample (material) , sampling (signal processing) , best response , statistical physics , mathematical optimization , computer science , nash equilibrium , repeated game , game theory , mathematical analysis , chemistry , physics , filter (signal processing) , chromatography , nonlinear system , quantum mechanics , machine learning , artificial intelligence , computer vision
We consider a model of evolution in games in which a revising agent observes the actions of a random number of randomly sampled opponents and then chooses a best response to the distribution of actions in the sample. We provide a condition on the distribution of sample sizes under which an iterated p ‐dominant equilibrium is almost globally asymptotically stable under these dynamics. We show under an additional condition on the sample size distribution that in supermodular games, an almost globally asymptotically stable state must be an iterated p ‐dominant equilibrium. Since our selection results are for deterministic dynamics, any selected equilibrium is reached quickly; the long waiting times associated with equilibrium selection in stochastic stability models are absent.