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 p_i (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, p_i may instead be a function of the difference between the parties' commitments to the contest. The Contest Success Function (CSF) for the difference from 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.In preparing successive drafts of this paper I have benefited from suggestions and comments from Michele Boldrin, Avinash Dixit, Arye L. Hillman, David Hirshleifer, Eric S. Maskin, David Levine, Eric Rasmusen, John G. Riley, Russell Roberts, and Leo K. Simon.