Evolution of Fighting Behaviour: The Effect of Variation in Resource ...

204 M. ENQUIST AND O. LEIMARIntroduce the stopping time T~' as the first fighting step for which X. n - S~', anddefine the stopping time T~ as equal to T~ when B uses S" (m = 1,..., M).Consider the following event (A's observation at step n): O.,x = {X A = x, TB > n - 1}.A must decide whether to give up or continue without yet knowing B's decision atthis step. This decision should be made so that A's utility is maximized. Let U,(x)denotes A's utility given the observation O..x. From the relation cAcn -- c 2 it followsthat the cost per step for A is CA = C exp (-0/2). It is now possible to set up aniteration for U.(x)'0.SE(VIO .... Ts=n) Pr(T~=nlO~.x);x