Meta-evolutionary Game Dynamics for Mathematical Modelling of Rules Dynamics

  • Takashi Hashimoto
  • Yuya Kumagai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2801)


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.


Dynamics of rules Mathematical modelling Meta-evolutionary game dynamics Replicator equations Evolutionary stable games 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Takashi Hashimoto
    • 1
    • 2
  • Yuya Kumagai
    • 1
  1. 1.School of Knowledge ScienceJapan Advanced Institute of Science and Technology (JAIST)IshikawaJapan
  2. 2.Language Evolution and Computation Research Unit, School of Philosophy, Psychology and Language SciencesUniversity of Edinburgh 

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