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Evolutionary Games and Matching Rules

Jensen , Martin Kaae and Rigos, Alexandros LU (2017) In Working Papers
Abstract
This study considers evolutionary models with non-uniformly random matching when interaction occurs in groups of n>=2 individuals. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy – and consequently long-run behavior in the population – varies with the frequencies of different group types. These frequencies crucially depend on the particular matching process at hand. Two new equilibrium concepts are introduced: Nash equilibrium under a matching rule (NEMR) and evolutionarily stable strategy under a matching rule (ESSMR). When matching is uniformly random, these reduce to Nash equilibrium and evolutionarily stable strategy, respectively.... (More)
This study considers evolutionary models with non-uniformly random matching when interaction occurs in groups of n>=2 individuals. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy – and consequently long-run behavior in the population – varies with the frequencies of different group types. These frequencies crucially depend on the particular matching process at hand. Two new equilibrium concepts are introduced: Nash equilibrium under a matching rule (NEMR) and evolutionarily stable strategy under a matching rule (ESSMR). When matching is uniformly random, these reduce to Nash equilibrium and evolutionarily stable strategy, respectively. Several results that are known to hold for population games under uniform random matching carry through to our setting. In our most novel contribution, we derive results on the efficiency of the Nash equilibria of population games and show that for any (fixed) payoff structure, there always exists some matching rule leading to average fitness maximization in NEMR. Finally, we provide a series of applications to commonly studied normal-form games. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
evolutionary game theory, evolutionarily stable strategy, ESS, non-uniformly random matching, C72, C73
in
Working Papers
issue
2017:11
pages
27 pages
publisher
Department of Economics, Lund University
language
English
LU publication?
yes
id
30bf17c1-2c8e-4709-9c0b-43dc85b73cef
alternative location
http://swopec.hhs.se/lunewp/abs/lunewp2017_011.htm
date added to LUP
2017-09-29 14:31:36
date last changed
2017-10-02 08:48:42
@misc{30bf17c1-2c8e-4709-9c0b-43dc85b73cef,
  abstract     = {This study considers evolutionary models with non-uniformly random matching when interaction occurs in groups of n>=2 individuals. In such models, groups with different compositions of individuals generally co-exist and the reproductive success (fitness) of a specific strategy – and consequently long-run behavior in the population – varies with the frequencies of different group types. These frequencies crucially depend on the particular matching process at hand. Two new equilibrium concepts are introduced: Nash equilibrium under a matching rule (NEMR) and evolutionarily stable strategy under a matching rule (ESSMR). When matching is uniformly random, these reduce to Nash equilibrium and evolutionarily stable strategy, respectively. Several results that are known to hold for population games under uniform random matching carry through to our setting. In our most novel contribution, we derive results on the efficiency of the Nash equilibria of population games and show that for any (fixed) payoff structure, there always exists some matching rule leading to average fitness maximization in NEMR. Finally, we provide a series of applications to commonly studied normal-form games.},
  author       = {Jensen , Martin Kaae  and Rigos, Alexandros},
  keyword      = {evolutionary game theory,evolutionarily stable strategy,ESS,non-uniformly random matching,C72,C73},
  language     = {eng},
  note         = {Working Paper},
  number       = {2017:11},
  pages        = {27},
  publisher    = {Department of Economics, Lund University },
  series       = {Working Papers},
  title        = {Evolutionary Games and Matching Rules},
  year         = {2017},
}