Mutation–selection equilibrium in games with mixed strategies Export

@article{citeulike:5314156, abstract = {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 × n payoff matrix. Players can use mixed strategies, which are given by the vector ( p 1 ,…, 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–Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.}, author = {Tarnita, Corina E. and Antal, Tibor and Nowak, Martin A.}, citeulike-article-id = {5314156}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.jtbi.2009.07.028}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0022519309003415}, day = {07}, doi = {10.1016/j.jtbi.2009.07.028}, issn = {00225193}, journal = {Journal of Theoretical Biology}, keywords = {game}, month = {November}, number = {1}, pages = {50--57}, posted-at = {2009-10-05 05:22:53}, priority = {2}, title = {Mutation–selection equilibrium in games with mixed strategies}, url = {http://dx.doi.org/10.1016/j.jtbi.2009.07.028}, volume = {261}, year = {2009} }

TY - JOUR ID - citeulike:5314156 L3 - citeulike-article-id:5314156 N2 - 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 × n payoff matrix. Players can use mixed strategies, which are given by the vector ( p 1 ,…, 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–Dove game. We prove general statements about the relationship between games with pure and with mixed strategies. IS - 1 JF - Journal of Theoretical Biology SN - 00225193 EP - 57 TI - Mutation–selection equilibrium in games with mixed strategies VL - 261 SP - 50 KW - game AU - Tarnita, Corina AU - Antal, Tibor AU - Nowak, Martin PY - 2009/11/07/ UR - http://dx.doi.org/10.1016/j.jtbi.2009.07.028 ER -