Promotion of cooperation by payoff noise in a $2\ifmmode\times\else\texttimes\fi{}2$ game

Promotion of cooperation by payoff noise in a $2 \times 2$ game

Jun Tanimoto

Phys. Rev. E 76, 041130 – Published 24 October 2007

Abstract

A series of numerical simulations of a $2 \times 2$ symmetric game on a network examined whether payoff matrix noise promotes cooperation, as reported initially by Perc [New J. Phys. 8, 22 (2006)]. Agents have no memory (they offer cooperation, $C$ , or defection, $D$ ). We assume that the network is time invariable. The effect of payoff matrix noise (PMN) is measured by a simulated payoff difference between a normal network game and a network game with PMN. The effect of PMN appears only when a local strategy adaptation is implemented (for example, a network game with imitation dynamics). The influence of PMN becomes more significant with a larger stochastic deviation, and less significant in a larger degree network. One reason for PMN’s effectiveness is the local strategy adaptation mechanism, which helps both the preservation and fixation of $C$ agents, and not that the payoff matrix noise makes a dilemma game into a Trivial (dilemma-free) game.