Multi-Population Replicator Dynamics with Changes of Interpretations of Strategies

Takafumi KANAZAWA  Toshimitsu USHIO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2717-2723
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2717
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Modelling, Systems and Simulation
evolutionary game,  replicator dynamics,  hybrid system,  interpretation function,  

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If some differences of perceptions arise between populations, then strategies which are regarded as the same strategy in a population may be perceived distinguishably in the other populations. To discuss such a situation, replicator dynamics for multi-population hypergames has been proposed. However, it is assumed that players' perceptions are given and fixed. In this paper, we consider that each population has various interpretation functions and choose one of them depending on payoffs, and we propose a hybrid system representation of replicator dynamics with changes of interpretation functions. Moreover, we apply our proposed model to a well-known example of a hypergame "Soccer Hooliganism" and show that behaviors converging to heteroclinic orbits can appear by the changes of the interpretation functions.