When several competitors deplete a patch, it can be advantageous for each of them to stay provided that others leave, whereas, on the other hand, staying longer decreases the expected payoff for everyone. This situation can be considered as a generalized war of attrition. Previous studies showed that when competitors interfere optimal patch leaving strategies become stochastic and the expected leaving time is much larger than predicted by the marginal value theorem.
The possibility of superparasitism, as occurs e.g. in parasitoids, induces such interference. In addition, it gives several complications. First, the payoff of females that have left the patch is affected by the ovipositions of the remaining individuals. Second, differences in arrival time of females cause payoff-relevant asymmetries, since females that arrived early have parasitised more hosts in a patch at the moment superparasitism starts than those that arrived late.
We show that this can be modelled as an asymmetric generalized war of attrition, and derive global characteristics of the ESS for simultaneous decisions when to start superparasitism and when to leave a patch.