Efficiency based strategy spreading in the prisoner's dilemma game
Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 8, 64289 Darmstadt, Germany
Corresponding author: a email@example.com
Revised: 12 January 2009
Published online: 21 May 2009
In contrast to well-mixed populations, discrete interaction patterns have been shown to support cooperation in the prisoner's dilemma game, and a scale-free network topology may even lead to a dominance of cooperation over defection. The majority of studies assumes a strategy adoption scheme based on accumulated payoffs. The use of accumulated payoffs, however, is incompatible with the integral property of the underlying replicator dynamics to be invariant under a positive affine transformation of the payoff function. We show that using instead the payoff per interaction to determine the strategy spread, which has been suggested recently and recovers the required invariance, results in fundamentally different dynamical behavior under a synchronized strategy adoption considered here. Most notably, in such an efficiency based scenario the advantage of a scale-free network topology vanishes almost completely. We present a detailed explanation of the fundamentally altered dynamical behavior.
PACS: 89.75.-k – Complex systems / 89.75.Hc – Networks and genealogical trees / 02.50.Le – Decision theory and game theory
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009