WAR OF ATTRITION WITH INDIVIDUAL-DIFFERENCES ON RHP

The fact that there always exists various kinds of almost continuous m utations for any animal population implies that players in competition s can never be perfectly symmetric in any sense. To develop a model to fit this reality, we consider war of attrition games in which players have continuously different resource holding potential (RHP). The RHP of each opponent is not known in our settings. Pure ESS functions and Nash equilibria are obtained under sufficiently rational conditions a s unique solutions of certain differential equations among the class o f Lebesgue measurable functions. They are normal in that a higher RHP induces a longer attrition time, which implies that a player with grea ter RHP always wins. This model includes as the limit the conclusions of Maynard Smith (1974, J. theor. Biol. 47, 209-221) and Norman et al. (1977, J. theor. Biol. 65, 571-578), which did not consider individua l differences in RHP. Our results suggest that, by changing each playe r's qualitative differences to continuous quantitative differences, so me of the mixed ESS solutions previously found in discrete games may d egenerate into pure ESS functions. Moreover, we found that the smaller the individual differences of RHP, the smaller is the mean pay-off of most individuals as well as the total pay-off of the population. (C) 1998 Academic Press