Testing for the Asymmetric War of Attrition When Only Roles and Fight Duration Are Known

In the asymmetric war of attrition the two opponents each play a different role. But mistakes in assumption of role are possible. Hammerstein and Parker (1982, J. theor. Biol.96, 647-682) investigated this game to calculate the ESS of the distribution of the cost (fight duration) the players should be prepared to pay. They show that players which think they assume the bad role should give up before a separation value s, while players which think they assume the good role should persist longer than s . In this paper this information is converted into the distribution of actual fight durations. This provides predictions which can be tested using a real data-set. To improve the possibility of testability, most criteria are built on two assumptions only: (i) roles can be assigned correctly, and (ii) the actual fight durations are known. Criteria are given to test which role is the good one, and to estimate the separation value s. If an estimate for s is found, tests can be performed to see whether or not it actually behaves as a separation value. Other criteria test if the distribution of actual fight durations could be generated by the ESS of the asymmetric war of attrition with linear costs. It is shown how the test can be used by comparing the predictions with a real data-set of the fighting behaviour of the yellow dungfly. Finally, comparing the predictions of the asymmetric war of attrition with the predictions of the asymmetric sequential assessment game, a striking resemblance is uncovered.