Game Theory in Evolution
http://www.cambridge.org/us/download_file/203311/
I started Rickard Dawkins’ The Selfish Gene in September. Coincidentally, on the same day that we learned Game Theory in class, Dawkins also introduced evolutionarily stable strategy (ESS) in his book. ESS means that if an entire population adopt such a strategy, then no mutant strategy can invade. Dawkins introduced the concept of symmetry games, that adversaries starting in similar situations with the same strategy can receive same payoffs. He used the dove-hawk game as an example: dove (threatened a little but never hurt the opponent) and hawk (fight hard but badly injured). With some oscillations around the number, a stable ratio of the two species will be reached when the average payoffs of them are equal. In an evolutionary sense, the payoff should be each species reproductive success. The ESS/dominant strategy of this game is the “retaliator”, who behaves like a hawk when he meets a hawk, like a dove when he meets a dove. In reality, ESS is less common in nature considering five aspects: “stability of the environment”, “nonlinear dynamics”, “interspecific ESS’s”, “speed of evolution” and “genetic constraints”. Therefore, it is complicated to calculate actual payoffs and to determine the establishment of an ESS.
There are many similarities between ESS and Nash Equilibrium. In fact, ESS is actually derived from NE according to John M. Smith and George R. Price “none of a number of players in a game can gain by changing her/his strategy unilaterally.” There can exist multiple ESS for a population. An ESS does not suggest the best strategy for an entire population either, since genes cannot predict actions beyond their current environment. The ratio of two species is the same as the mixed strategy equilibrium. As we learned in class, the NE is calculated by setting the expected payoffs of player A equal to that of player B. The same dove-hawk example connects Dawkins’ evolution theory with the material we learned in class. It is surprising to see how widely applicable game theories are and how it can be used in seemingly unrelated contexts.