Asymptotically stable equilibrium and limit cycles in the Rock–Paper–Scissors game in a population of players with complex personalities

Tadeusz Platkowski and Jan Zakrzewski

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 23, 4219-4226

Abstract: We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model.

Keywords: Rock–Paper–Scissors game; Population dynamics; Asymptotic stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:23:p:4219-4226

DOI: 10.1016/j.physa.2011.06.041

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