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.
| Original language | English (US) |
|---|---|
| Article number | 75 |
| Journal | Electronic Journal of Probability |
| Volume | 19 |
| DOIs | |
| State | Published - Aug 19 2014 |
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Keywords
- Bootstrap percolation
- Evolutionary stable strategy
- Interacting particle systems
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
Evolutionary games on the lattice : Best-response dynamics. / Evilsizor, Stephen; Lanchier, Nicolas.
In: Electronic Journal of Probability, Vol. 19, 75, 19.08.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Evolutionary games on the lattice
T2 - Best-response dynamics
AU - Evilsizor, Stephen
AU - Lanchier, Nicolas
PY - 2014/8/19
Y1 - 2014/8/19
N2 - 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.
AB - 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.
KW - Bootstrap percolation
KW - Evolutionary stable strategy
KW - Interacting particle systems
UR - http://www.scopus.com/inward/record.url?scp=84907304191&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84907304191&partnerID=8YFLogxK
U2 - 10.1214/EJP.v19-3126
DO - 10.1214/EJP.v19-3126
M3 - Article
AN - SCOPUS:84907304191
VL - 19
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
M1 - 75
ER -