title: Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.
abstract: Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.
authors.affiliation: School of Economics, Wuhan University of Technology, Wuhan, 430070, China.
authors.forename: Qian
authors.initials: Q
authors.lastname: Yu
authors.affiliation: School of Economics and Management, Wuhan University, Wuhan, 430072, China.
authors.forename: Debin
authors.initials: D
authors.lastname: Fang
authors.affiliation: Department of Public Policy, City University of Hong Kong, Hong Kong, China.
authors.forename: Xiaoling
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Department of Economics, The George Washington University, Washington DC, 20052, United States.
authors.forename: Chen
authors.initials: C
authors.lastname: Jin
authors.affiliation: School of Economics and Management, Wuhan University, Wuhan, 430072, China.
authors.forename: Qiyu
authors.initials: Q
authors.lastname: Ren
mesh_terms: D005075:Biological Evolution; D003643:Death; D005716:Game Theory; D006801:Humans; D011156:Population Density; D011336:Probability; D012641:Selection, Genetic / Q000235:genetics; D013269:Stochastic Processes