Replicator Dynamics with Government's Intervention by Collection and Reallocation of Payoffs

Takafumi KANAZAWA  Toshimitsu USHIO  Hayato GOTO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.10   pp.2170-2177
Publication Date: 2007/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.10.2170
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Nonlinear Phenomena and Analysis
replicator dynamics,  intervention,  payoff collection,  payoff reallocation,  

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In a community which consists of a large number of people interacting with each other, social dilemma is an important problem. This problem occurs when the payoff of each person conflicts with the total payoff of the community which he/she belongs to. Evolutionary game theory has been used as a powerful mathematical framework to analyze such a social problem. Recently, the authors have proposed replicator dynamics with reallocation of payoffs. In this model, the government is willing to lead the population to a desirable goal state by using collections and reallocations of payoffs. In this paper, we investigate this model, and show conditions for the goal state to be a locally or a globally asymptotically stable equilibrium point, respectively. We also propose a government's strategy depends on population states which can stabilize the goal state globally.