Resistance is useless?--Extensions to the game theory of kleptoparasitism

We extend the game theoretic model of kleptoparasitism introduced by Broom and Ruxton (1998, Behav. Ecol. 9, 397-403) in two ways: we allow for asymmetric contests, where the probability alpha of the challenger winning can take any value from 0 to 1; and we allow the handler to choose not to resist the challenge, but to immediately concede and relinquish its food to the challenger. We find, in general, three possible evolutionarily stable strategies--challenge-and-resist (Hawk), challenge-but-do-not-resist (Marauder) and do-not-challenge-but-resist (Retaliator). When alpha = 1/2, we find that Hawk and Marauder are the only ESS's, in contrast to the result of the original model; we also find an overlap region, in parameter space, where two different ESS's are possible, depending on initial conditions. For general alpha, we see that all three ESS are possible, depending on different values of the environmental parameters; however, as the average time of a contest over food becomes long, then the Marauder strategy becomes more and more prevalent. The model makes a potentially significant prediction about animal behaviour in the area of kleptoparasitism, that a searcher, when it meets a handler, will only decline to attack that handler when alpha < 1/2 i.e. when the defender is more likely to win. One possible converse of this statement, that a handler whose probability of success is greater than 1/2 should always resist a challenge, is not true.