  The war of attrition in game theory is a model of a stand-off situation
between two opponents where the winner is determined by its persistence. We
model a stand-off between a predator and a prey when the prey is hiding and the
predator is waiting for the prey to come out from its refuge, or when the two
are locked in a situation of mutual threat of injury or even death. The
stand-off is resolved when the predator gives up or when the prey tries to
escape. Instead of using the asymmetric war of attrition, we embed the
stand-off as an integral part of the predator-prey model of Rosenzweig and
MacArthur derived from first principles. We apply this model to study the
coevolution of the giving-up rates of the prey and the predator, using the
adaptive dynamics approach. Some results are the same as for the asymmetric war
of attrition, but others are quite different.
