A Resource Allocation Problem

We consider a amount of model in which players must divide a fixed amount of resource between a number of trials of an underlying contest. A sufficient condition for the existence of a unique ES set (a simple generalization of the idea of an Evolutionarily Stable Strategy) is given in terms of the payoff function of the underlying contest, and it is shown that this condition implies that the stable strategies ignore the ordering of the trials. Two examples are given to illustrate the range of behaviour possible with different payoff functions in the underlying contest.