在弱选择及突变Moran过程下的演化博弈策略占优研究

On study of strategy dominance in evolutionary games under the weak selection and mutation with Moran process

研究了有限N种群博弈在策略突变、弱选择和Moran过程下的策略占优问题,主要讨论了创新性学习和模仿性学习两种机制下的两策略(A,B)演化博弈结果。我们发现,策略占优与博弈支付矩阵(a b c d)和种群数量相关:在创新性学习模型中,当且仅当1/2(a+b-c-d)N-a+d>0,策略A占优;当N>>0,当且仅当a+b>c+d,策略A冒险占优。在模仿性学习中,当(d-b)/(a-b-c+d)<1/3且N≥6时,A策略占优。

Evolutionary game theory is a mathematical tool to study the evolution of strategies. In this paper, we study strategy dominance problems in evolutionary games under the weak selection and mu- tation with Moran process in N finite population. We mainly discuss evolutionary games with two strategies {A,B} We find that the strategy dominance is related to the game payoff matrix and the number N of population ： In creative learning model, the strategy A dominates B if and only if 1/2（a ＋b-c-d）N-a＋d 〉0,and whenN 〉 〉 O,A is adventure dominant if and only ifa ＋ b 〉 c ＋ d. In theimitation learning , strategy A dominates B when d-b/a-b-c＋d〈1/3andN≥6.