TY - JOUR
T1 - Evolutionary games in space
AU - Kronik, N.
AU - Cohen, Y.
PY - 2009/1
Y1 - 2009/1
N2 - The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop the strategy dynamics for such surfaces. When the surfaces are locally stable, but not homogenous, the standard definitions of ESS and the maximum principle fall apart. Yet, we show by examples that strategy dynamics leads to convergent stable inhomogeneous strategies that are possibly ESS, in the sense that for many scenarios which we simulated, invaders could not coexist with the exisiting strategies.
AB - The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop the strategy dynamics for such surfaces. When the surfaces are locally stable, but not homogenous, the standard definitions of ESS and the maximum principle fall apart. Yet, we show by examples that strategy dynamics leads to convergent stable inhomogeneous strategies that are possibly ESS, in the sense that for many scenarios which we simulated, invaders could not coexist with the exisiting strategies.
KW - G-function
KW - evolutionary ecology
KW - game theory
KW - mathematical modeling
KW - reaction-diffusion equation
UR - http://www.scopus.com/inward/record.url?scp=79960788416&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79960788416&partnerID=8YFLogxK
U2 - 10.1051/mmnp/20094602
DO - 10.1051/mmnp/20094602
M3 - Article
AN - SCOPUS:79960788416
SN - 0973-5348
VL - 4
SP - 54
EP - 90
JO - Mathematical Modelling of Natural Phenomena
JF - Mathematical Modelling of Natural Phenomena
IS - 6
ER -