Multi-Population Replicator Dynamics with Erroneous Perceptions

Takafumi KANAZAWA  Toshimitsu USHIO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2857-2865
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2857
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
evolutionary game,  evolutionarily stable strategy,  replicator dynamics,  perception,  chicken game,  

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In evolutionary game theory, to the best of our knowledge, individuals' perceptions have not been taken into consideration explicitly. When an individual interacts with the other individual under coexistence of heterogeneous sub-populations, the individual may be willing to change his/her strategy depending on the sub-population the other individual belongs to. Moreover, in such a situation, each individual may make an error about the sub-population the other individual belongs to. In this paper, we propose a multi-population model with such erroneous perceptions. We define an evolutionarily stable strategy (ESS) and formulate replicator dynamics in this model, and prove several properties of the proposed model. Moreover, we focus on a two-population chicken game with erroneous perceptions and discuss characteristics of equilibrium points of its replicator dynamics.