Non-local interactions in spatial evolutionary games

Thumbnail Image
Date
2013-01-01
Authors
Aydogmus, Ozgur
Major Professor
Advisor
Zhijun Wu
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract

As a special case of symmetric game in which the players share a common payoff matrix, evolutionary game provides a suitable approach to model and explore the emergence of cooperative behavior in natural and social systems. The evolutionary spatial game (ESG) further specifies the payoff for each individual by both the payoff matrix $M$ and the spatial dependence structure of the population on a geophysical domain. Two players game serves as a foundation of modeling various biological/social interactive systems and provides a great amount of interesting game theoretical models such as prisoner's dilemma game, snow drift game etc.

We formulate a two players evolutionary spatial game under the framework of initialization, effective local payoff, and the Markov chain for strategy update. The spatial dependence structure is modeled by a probability distribution parameterized by the dependence geometry and strength in the neighborhood of each location. Particularly, we study the structure based on Gaussian process. Computational methods are proposed and applied to study the convergence of simulations. In addition, limiting non-local differential equation is introduced and analysed in terms of spreading speeds and traveling waves.

Comments
Description
Keywords
Citation
DOI
Source
Subject Categories
Copyright
Tue Jan 01 00:00:00 UTC 2013