Dynamics Days 2003
XXIII annual conference -4 decades of chaos 1963-2003-
http://www.imedea.uib.es/~ddays/

Palma de Mallorca, Spain
24-27 September

Studying Coevolution of Rules and Behaviour with Extended
Replicator System

(Poster Session)

Takashi Hashimoto and Yuya Kumagai

Japan Advanced Institute of Science and Technology Abstract: We aim at
proposing  a new  class  of dynamical  systems  for understanding  the
dynamics  of  social  rules  and  individual  behaviour  by  extending
replicator  equations, in  which payoff  matrix of  evolutionary games
change dynamically.  After summarizing two  views of social  rules, as
game forms  and as  equilibria of games,  we address a  perspective to
integrate them and formalize it mathematically.

A new  approach proposed  here is an  integrated version of  above two
views.  We  basically express  initial  rules  in  a society  by  game
forms. Multiple games are  introduced explicitly, which have their own
weights  representing the  extent  of importance  of  the rules.  Each
player plays  all games  with one strategy  and gains  weighted payoff
from each  game. The population  of strategies varies in  time through
the payoffs. In addition, the weights of the games change depending on
the  payoffs and  the  population  of strategies.  The  change of  the
weights  is  governed by  another  rule,  so-called  a meta-rule.  The
weighted sum of all games can be considered as indicating a whole rule
in the society.  Accordingly, this whole rule shifts continuously, not
discretely as transition among equilibria.

Computer simulations  of an example  of the model show  the punctuated
change  of  strategy  distributions,  the transitions  of  a  dominant
strategy,   and  the   metastable  state   different  from   the  Nash
equilibrium. We  introduce an idea of evolutionary  stability of games
for analyzing this system.