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Evolutionary games on the lattice: best-response dynamics

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Evolutionary games on the lattice: best-response dynamics
2.	Creator	Author's name, affiliation, country	Stephen Evilsizor; Arizona State University; United States
2.	Creator	Author's name, affiliation, country	Nicolas Lanchier; Arizona State University; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Interacting particle systems, evolutionary game, evolutionary stable strategy.
3.	Subject	Subject classification	60K35, 91A22
4.	Description	Abstract	The best-response dynamics is an example of an evolutionary game where players update their strategy in order to maximize their payoff. The main objective of this paper is to study a stochastic spatial version of this game based on the framework of interacting particle systems in which players are located on an infinite square lattice. In the presence of two strategies, and calling a strategy selfish or altruistic depending on a certain ordering of the coefficients of the underlying payoff matrix, a simple analysis of the nonspatial mean-field approximation of the spatial model shows that a strategy is evolutionary stable if and only if it is selfish, making the system bistable when both strategies are selfish. The spatial and nonspatial models agree when at least one strategy is altruistic. In contrast, we prove that in the presence of two selfish strategies and in any spatial dimension, only the most selfish strategy remains evolutionary stable. The main ingredients of the proof are monotonicity results and a coupling between the best-response dynamics properly rescaled in space with bootstrap percolation to compare the infinite time limits of both systems.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF
7.	Date	(YYYY-MM-DD)	2014-08-19
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/3126
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-3126
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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