Evolutionary equilibrium strategies.

Abstract This paper re-examines the concept of evolutionary stability proposed by Maynard Smith. For any finite population it is shown that a strategy which is stable in the sense of Maynard Smith may have a lower fitness than a mutant strategy regardless of the proportion of contestants using the latter. Two alternative concepts of evolutionary stability are then proposed. A strategy is described as being strongly stable if no mutant is able to invade because of its higher fitness and weakly stable if it has a higher fitness whenever the contestants using any particular mutant strategy become sufficiently numerous. For the “war of attrition” between contestants of a given species Maynard Smith and others have argued that the evolutionarily stable strategy is for a contestant to bid (for food or territory) by attempting to wait out its opponent according to an exponential mixed strategy. This paper establishes that such a strategy is only weakly stable and that for any number n there exists a mutant strategy with a higher fitness until the number of mutants in the population exceeds n . The final section reconsiders the stability issue when a natural informational asymmetry is introduced. Each contestant is assumed to be uncertain as to the value its opponent places on the object over which they are competing. In contrast to the symmetric case it is shown that there is a strategy which is strongly stable with respect to any feasible mutant as long as the population is sufficiently large.