Conflict and rent-seeking success functions: Ratio vs. difference models of relative success

The rent-seeking competitions studied by economists fall within a much broader category of conflict interactions that also includes military combats, election campaigns, industrial disputes, lawsuits, and sibling rivalries. In the rent-seeking literature, each party’s success p1 (which can be interpreted either as the probability of victory or as the proportion of the prize won) has usually been taken to be a function of the ratio of the respective resource commitments. Alternatively, however, p1 may instead be a function of the difference between the parties’ commitments to the contest. The Contest Success Function (CSF) for the difference form is a logistic curve in which, as is consistent with military experience, increasing returns apply up to an inflection point at equal resource commitments. A crucial flaw of the traditional ratio model is that neither onesided submission nor two-sided peace between the parties can ever occur as a Cournot equilibrium. In contrast, both of these outcomes are entirely consistent with a model in which success is a function of the difference between the parties’ resource commitments.