Eur. Phys. J. B 69, 599-603 (2009)
https://doi.org/10.1140/epjb/e2009-00177-4

Efficiency based strategy spreading in the prisoner's dilemma game

Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 8, 64289 Darmstadt, Germany

Corresponding author: ^a porto@fkp.tu-darmstadt.de

Received: 25 November 2008
Revised: 12 January 2009
Published online: 21 May 2009

Abstract

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.