7th European Conference on Artificial Life (ECAL 2003),
Dortmund, Germany, September 14-17, 2003
http://www.ecal2003.org/

Meta-evolutionary  game dynamics  for mathematical  modeling
of rules dynamics

Takashi Hashimoto and Yuya Kumagai

This  paper  proposes  an evolutionary-game-theory  model,  called
meta-evolutionary  game  dynamics, for  studying  the dynamics  of
rules  and  individual behaviour.   Although  there  are two  game
theoretical views of  rules, i.e., seeing rules as  game forms and
as  equilibria of  games,  endogenous changes  of  rules are  not
modelled effectively by either of these two views.  We introduce a
model  for integrating  the two  views, in  which  the interaction
rules  of  replicator   equations  change  dynamically.   Computer
simulations of an  example of the model that  include mutation and
extinction of  both strategies and games show  (1) an intermittent
change of strategy distributions,  (2) a continual transition from
a dominant strategy to another, and (3) metastable states distinct
from the Nash equilibria.   We discuss the notion of evolutionary
stability  of  games  and   some  natural  examples  showing  rule
dynamics.   We  conclude   that  meta-evolutionary  game  dynamics
enables the study of the  endogenous dynamic of rules.  Our model
contributes, therefore, the development of game theory approach to
the dynamics of rules.