Dynamic evolutionary game related to elementary large games and

Dynamic evolutionary game related to elementary large games and

SUB Gfittingen
215 196 554
Krzysztof Argasinski
Dynamic evolutionary game
related to elementary large games and
replicator dynamics *
Nr 955
Warszawa, April 2003
Abstract
This article contains construction of multipopulation evolutionary game based on elementary
large games and replicator dynamics. For this purpose a multipopulation model with payoff depending of interspecific proportions (metasimplex concept) was developed. Article also contains
. a cpmparson of classical evolutionary game theory solutions with a new theory.
Keywords: evolutionary eqilibrium, evolutionary stable states, metasimplex, multipopulation models, elementary large games
Dynamiczna gra ewolucyjna zwi^zana z duzymi grami i dynamik^ replikatorowq.
Streszczenie
Praca zawiera konstrukcje wielopopulacyjnej gry ewolucyjnej opartej o aparat elementamych
duzych gier i dynamikq replikatorowq. Do tego celu wykorzystano model wielopopulacyjny
uwzgledniajacy zmienaosc proporcji miedzygatunkowych (koncepcja metasympleksu). W pracy
znajduje sie rowniez porownanie powstalego aparatu z rozwiazaniami klasycznej teorii gier
ewolucyjnych.
Siowa kluczowe: rownowaga ewolucyjna, stan ewolucyjnie stabilny, metasympleks, modele
wielopopulacyjne, duze gry
* RESEARCH SUPPORTED BY KBN GRANT # 5 H02B 008 20
Contents
1. Basic definitions and static characterizations of evolutionary stability
3
2. Replicator dynamics
5
3. Modifications of basic evolutionary game model
>-'
7
3.1.Multipopulation models
7
3.2. Critical remarks on multipopulation models
9
3.3. Density dependent models
12
3.4. Density and interspecific proportion dependent models
13
4. Elementary large games
16
5. Replicator dynamics for large games
19
5.1. Static characterizations based on elementary large games
19
5.2. Replicator dynamics for extended large games
26
5.3.Basic differences between classical evolutionary game theory and "large games" 29
Summary, appendix, bibliography
31