Open AccessDeterministic equations for stochastic spatial evolutionary games
Author(s) -
Hwang SungHa,
Katsoulakis Markos,
ReyBellet Luc
Publication year - 2013
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/te829
Subject(s) - replicator equation , ordinary differential equation , domain (mathematical analysis) , computer science , evolutionary game theory , population , mathematics , identification (biology) , selection (genetic algorithm) , mathematical optimization , differential equation , mathematical economics , game theory , mathematical analysis , artificial intelligence , ecology , demography , sociology , biology
Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of the strategy profile of individuals over space. We derive integro‐differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics and provide powerful tools for investigating the problem of equilibrium selection. Deterministic equations allow the identification of many interesting features of the evolution of a population's strategy profiles, including traveling front solutions and pattern formation.