Mutation in evolutionary games can increase average fitness at equilibrium.
We study game dynamical interactions between two strategies, A and B, and analyse whether the average fitness of the population at equilibrium can be increased by adding mutation from A to B. Classifying all two by two games with payoff matrix [(a,b),(c,d)], we show that mutation from A to B enhances the average fitness of the whole population (i) if both a and d are less than (b + c)/2 and (ii) if c is less than b. Furthermore, we study conditions for maximizing the productivity of strategy A, and we analyse the effect of mutations in both directions. Depending on the biological system, a mutation in an evolutionary game can be interpreted as a genetic alteration, a cellular differentiation, a change in gene expression, an accidental or deliberate modification in cultural transmission, or a learning error. In a cultural context, our results indicate that the equilibrium payoff of the population can be increased if players sometimes choose the strategy with lower payoff. In a genetic context, we have shown that for frequency-dependent selection mutation can enhance the average fitness of the population at equilibrium.
Willensdorfer
Martin
M
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA.
Nowak
Martin A
MA
D000818:Animals; D005075:Biological Evolution; D005260:Female; D005716:Game Theory; D008297:Male; D008954:Models, Biological; D009154:Mutation