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Evolutionary Games
ABSTRACT The evolutionary game has to do with the survival of a given strategy within a population of individuals using potentially many different strategies. It is not unlike a mathematical game in the sense that it has players (individual organisms), strategies (heritable phenotypes), strategy sets (strategies available to a particular organism), and payoffs (individual fitness). An organism’s strategy is passed on from generation to generation. In so doing, the organism’s fitness, as a function of all strategies used in the population, determines how its strategy frequency changes within the population. The solution to the evolutionary game, as formulated by Maynard Smith, is a strategy that is resistant to invasion by alternative strategies and is called an evolutionarily stable strategy (ESS). The G-function method for finding an ESS is presented. The ESS solution for several games along with group optimal and Nash solutions are presented in order to illustrate the ESS concept and how it differs from traditional game solutions. We begin with familiar matrix games and show how they can be put into an evolutionary game setting. Two communication network games, the forwarder's dilemma game and the multiple access game, are formulated as evolutionary games to demonstrate the approach and solution methods. We then generalize the forwarder's dilemma game in terms of a cost-benefit game and show how cooperation can evolve in such a game. This will involve many interesting features of the adaptive landscape associated with evolutionary games. These include convergent stable maximums and minimums, unstable maximums and minimums, speciation, and ESS coalitions of more than one strategy. We conclude with a brief look at additional applications ranging from modeling cancer to the evolution of coexistence in flour beetles. |
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