Hawks, doves, and mixed-symmetry games

The hawk-dove game has proved to be an important tool for understanding the role of aggression in social interactions. Here, the game is presented in a more general form (GHD) to facilitate analyses of interactions between in dividuals that may differ in "size", where size is interpreted as a surroga te for resource holding power. Three different situations are considered, b ased on the availability and use of information that interacting individual s have about their sizes: the classical symmetric case, in which no informa tion about sizes is used, the asymmetric case, in which the individuals kno w their relative sizes and thus their chances of prevailing in combat, and a mixed-symmetry case, in which each individual only knows its own size (or only knows its opponent's size). I describe and use some recently develope d methods for multitype games-evolutionary games involving two or more cate gories of players. With these methods and others, the evolutionarily stable strategies (ESSs) that emerge for the three different cases are identified and compared. A proof of the form and uniqueness of the-ESS for the mixed- symmetry case is presented. In this situation, one size category at most ca n play a mixed strategy; larger individuals are aggressive and smaller indi viduals are not. As the number of size categories approaches infinity and t he size distribution becomes continuous, there is a threshold size, above w hich all individuals are aggressive, and below which they are not. (C) 2000 Academic Press.