Physica A 433 (2015) 367–378 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Heterogeneity of inferring reputation probability in cooperative behaviors for the spatial prisoners’ dilemma game Peng Lu a,b,* , Fang Wang c a Department of Automation, Tsinghua University, China b Department of Sociology, Tsinghua University, China c Department of Energy and Environment, Columbia University, United States highlights • This paper investigates the heterogeneity of inferring reputation, which is not adequately revealed before. • The effect of inferring reputation probability is decomposed into two parts, the mean effect and the heterogeneity effect. • The mean merely enhances cooperation as it is smaller, and undermines cooperation when it is larger. • The heterogeneity does not influence cooperation on the whole range of mean, but reduces cooperation with a smaller mean and propels cooperation with a larger mean. article info Article history: Received 9 January 2015 Received in revised form 17 March 2015 Available online 1 April 2015 Keywords: Heterogeneity Inferring reputation Probability Cooperative behaviors Spatial Prisoners’ dilemma game abstract As an important mechanism designed to counteract temptation and promote cooperation, reputation is widely investigated in the spatial Prisoners’ dilemma game. Existing research assumes that each agent imitates the neighbor that has the highest reputation with an inferring reputation probability p i , which is heterogeneous and enhances cooperation to some extent. So far the effect of heterogeneity has not been adequately revealed. There- fore, we will inspect the heterogeneity effect on a square lattice where agents play the prisoners’ dilemma game. It is assumed that the inferring reputation probability is nor- mally distributed, and its mean p and standard deviation sd represent its mean effect and heterogeneity effect on cooperation. Simulation results demonstrate that the mean or over- all effect on cooperation fits a nonlinear relationship. It promotes cooperation substantially as the mean is smaller (p < 0.5), it stabilizes cooperation at a stable state as the mean is in the middle range, and it undermines cooperation while p is larger (p > 0.8). The hetero- geneity effect varies with p as well: In the whole range of p, sd neither promotes nor reduces cooperation. However, heterogeneity reduces cooperation when p is smaller (p < 0.5), but turns to increasing cooperation when it grows larger (p > 0.5). © 2015 Elsevier B.V. All rights reserved. 1. Introduction As cooperation is vital for the human society, promoting it becomes a permanent pursuit for scientists [1–9]. Related solutions and models have been proposed to promote cooperation [1–62]. As the temptation seduces individuals to defect and therefore reduces cooperation [1,10], the core idea is to develop mechanisms overcoming the temptation that leads to * Corresponding author at: Department of Automation, Tsinghua University, China. E-mail address: lvpeng.tsinghua@hotmail.com (P. Lu). http://dx.doi.org/10.1016/j.physa.2015.03.053 0378-4371/© 2015 Elsevier B.V. All rights reserved.