Evolutionary Games in Space

N. Kronik; Y. Cohen

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 6, page 54-90
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Kronik, N., and Cohen, Y.. "Evolutionary Games in Space." Mathematical Modelling of Natural Phenomena 4.6 (2009): 54-90. <http://eudml.org/doc/222357>.

@article{Kronik2009,
abstract = { 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. },
author = {Kronik, N., Cohen, Y.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {mathematical modeling; game theory; reaction-diffusion equation; G-function; evolutionary ecology; -function; evolutionarily stable strategies},
language = {eng},
month = {11},
number = {6},
pages = {54-90},
publisher = {EDP Sciences},
title = {Evolutionary Games in Space},
url = {http://eudml.org/doc/222357},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Kronik, N.
AU - Cohen, Y.
TI - Evolutionary Games in Space
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/11//
PB - EDP Sciences
VL - 4
IS - 6
SP - 54
EP - 90
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.
LA - eng
KW - mathematical modeling; game theory; reaction-diffusion equation; G-function; evolutionary ecology; -function; evolutionarily stable strategies
UR - http://eudml.org/doc/222357
ER -

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