Mutation-selection equilibrium in games with mixed strategies

作者：Tarnita Corina E^*; Antal Tibor; Nowak Martin A

来源：Journal of Theoretical Biology, 2009, 261(1): 50-57.

DOI：10.1016/j.jtbi.2009.07.028

• Evolutionary dynamics
• Evolutionary game theory
• Finite population size
• Stochastic process
• Hawk-Dovegame

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n x n payoff matrix. Players can use mixed strategies, which are given by the vector (p(1,) p(2), ... , p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S(n). We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dovegame. We prove general statements about the relationship between games with pure and with mixed strategies.

• 出版日期2009-11-7