Selten (1980, J. theor. Biol. 84, 93(N)
/01) has shown that mixed strategies cannot be evolutionarily stable in asymmetric games. Because every interaction features some asymmetry, this result apparently precludes mixed strategies in an evolutionary setting. In Maynard Smith's Hawk}Dove game (1982, Evolution and the theory of games (UP-Cambridge), for example, Selten's result restricts attention to pure-strategy evolutionarily stable outcomes in which the animals use the ability to condition their actions on asymmetries to coordinate, with one playing Hawk and one playing Dove, and with con#icts in which both animals play Hawk never arising. This result contrasts with the intuition that the mixed equilibrium of the Hawk}Dove game captures important aspects of many animal interactions, including the possibility of con#ict. In this paper, we follow Eshel and Sansone (1995, J. theor. Biol. 177, 341}356) in enriching Selten's model to incorporate an important aspect of animal interactions, namely that payo!s and asymmetries may both be imperfectly observed. In the richer model, we "nd conditions under which e!ectively mixed strategies are stable in asymmetric games, as well as conditions under which they are not stable. Behavior will be conditioned on asymmetries, leading to pure-strategy equilibria in which con#ict is avoided, when there are relatively large, observable asymmetries and small observable variations in payo!s. Under opposite conditions, evolutionarily stable equilibria will appear that are e!ectively mixed, including the potential for con#ict. 2001 Academic Press 2.2. EVOLUTIONARY GAMES Maynard Smith proposed a model of an evolutionary game in which pairs of animals are 2 K. BINMORE AND L. SAMUELSON