# Evolutionary Games in Space

Mathematical Modelling of Natural Phenomena (2009)

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

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topKronik, 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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