Is the Predicted ESS in the Sequential Assessment Game Evolvable?

Abstract. The Sequential Assessment Game model of animal contests predicts an evolutionarily stable strategy (ESS) that is a sequence of thresholds for giving up. Simulated evolution experiments reveal that the selection pressure on higher-numbered thresholds is most likely too low to allow for the theoretically predicted ESS to evolve in nature. 1 Simulating the Sequential Assessment Game In game-theoretic models of animal contests, contestants are treated as players whose objective is to maximize their expected number of offspring. A strategy is a prescription of how a player should behave in every possible situation. A strategy S is evolutionarily stable, or an ESS, if a population of players that all follow S cannot be invaded by a mutant strategy S ′ [2]. Being an ESS is only a necessary condition for a strategy to actually evolve. Simulated evolution can be used to investigate whether theoretically predicted ESS’s are indeed evolvable. The objective in the classical Sequential Assessment Game of Enquist and Leimar [1] is to gain access to a resource. The game proceeds in succesive bouts