title: Evolutionary prisoner's dilemma game on graphs and social networks with external constraint.
abstract: A game-theoretical model is constructed to capture the effect of external constraint on the evolution of cooperation. External constraint describes the case where individuals are forced to cooperate with a given probability in a society. Mathematical analyses are conducted via pair approximation and diffusion approximation methods. The results show that the condition for cooperation to be favored on graphs with constraint is b¯/c¯>k/A¯ (A¯=1+kp/(1-p)), where b¯ and c¯ represent the altruistic benefit and cost, respectively, k is the average degree of the graph and p is the probability of compulsory cooperation by external enforcement. Moreover, numerical simulations are also performed on a repeated game with three strategies, always defect (ALLD), tit-for-tat (TFT) and always cooperate (ALLC). These simulations demonstrate that a slight enforcement of ALLC can only promote cooperation when there is weak network reciprocity, while the catalyst effect of TFT on cooperation is verified. In addition, the interesting phenomenon of stable coexistence of the three strategies can be observed. Our model can represent evolutionary dynamics on a network structure which is disturbed by a specified external constraint.
authors.affiliation: Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi׳an, Shaanxi 710027, China. Electronic address: huizhang06@gmail.com.
authors.forename: Hui
authors.initials: H
authors.lastname: Zhang
authors.affiliation: Yantai Institute of Coastal Zone Research, CAS, Yantai 264003, China.
authors.forename: Meng
authors.initials: M
authors.lastname: Gao
authors.affiliation: School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Lanzhou, Gansu 730000, China.
authors.forename: Wenting
authors.initials: W
authors.lastname: Wang
authors.affiliation: School of Mathematics and Information Sciences, Henan University, Kaifeng, Henan 475001, China.
authors.forename: Zhiguang
authors.initials: Z
authors.lastname: Liu
mesh_terms: D005716:Game Theory; D011329:Prisoners; D012944:Social Support
keywords: Diffusion approximation; Evolution of cooperation; External enforcement; Network structure; Pair approximation