We have created and analyzed a model for kleptoparasitic interactions when
individuals decide on the level of aggression in which they want to engage in the
contest over a resource item. The more aggressive each individual is relative
to an opponent, the higher are the chances of winning the item, but also
the higher is the cost of the interaction for that individual. We consider a
general class of cost functions and show that for any parameter values, i.e., for
any maximal potential level of aggression of the individuals, any value of
the resource and any type of the cost function, there is always a unique
Nash equilibrium. We identify four possible kinds of Nash equilibria and
give precise conditions for when they occur. We find that nonaggressive
behavior is not a Nash equilibrium even when the cost function is such that
aggressive behavior yields lower payoffs than avoiding the conflict altogether.
