Noise-induced sustainability of cooperation in Prisoner's Dilemma game

Abstract

Based on the concept of stochastic Prisoner’s Dilemma (SPD) game in experimental economics proposed by Bereby-Meyer and Roth (Am Econ Rev 96 (2006) 1029–1042) (see also H. Kunreuther et al., Judgm. Decis. Mak. 4 (5) (2009) 363–384), the dynamical properties of the SPD game is investigated in this paper. For the non-repeated SPD game, we can see that the increase of noise intensity will not only lead to loss of the stochastic stability of the boundary state corresponding to defection but also the non-equilibrium phase transition of the quasi-stationary distribution of the system, and that the fixation probability of cooperation will increase with the increase of noise intensity. However, for the stochastic TFT-AllD game, the increase of noise intensity will lead to the loss of the stochastic stability of the two boundaries corresponding to cooperation and defection respectively, but will not lead to the non-equilibrium phase transition of the quasi-stationary distribution of the system. Moreover, as a special case of the stochastic TFT-AllD game (i.e., (m−1)(b−c)=2c), we show that the fixation probability of TFT will increase (decrease) with the increase of noise intensity if the initial frequency of TFT is less (or larger) than 1/2.