Large mutations in asymmetric games
08/6/27, 13:30 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)
Evolutionary game theory introduced other solutions of games than traditional ESS theory. An ESS may not be convergence stable or continuous traits may show evolutionary branching when we consider evolutionary dynamics of continuous traits. These evolutionary game models are based on the assumption that a mutant's trait is not so different from its parent's one. However, it is not always true, we sometimes see children who are not similar to their parents. A previous work showed that variation maintained by mutation or other factors brings high cooperation in an iterated prisoner's dilemma game in which high cooperation never evolves without these fluctuations. We need to consider other cases with large mutations, which produce irregular offspring, and hence bring variation in the population. In this research we analyze evolution of continuous traits, which represents the probabilities choosing one option in asymmetric 2x2 games. Traits distribute broadly at evolutionary equilibrium with mutations and their means are near Nash equilibrium when mutation rates are extremely low or when mutations are very small according to the previous models. We discovered that the evolutionary outcome is surprisingly sensitive to the presence of large mutations; the evolutionary outcomes with large rare mutations are no longer predictable by the Nash equilibrium calculated without mutation. If most mutants are close to the original type but very small fraction of mutants are widely distributed, the evolutionary equilibrium might depend on very rare mutants with wide distribution.
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