Effort Levels in Contests with Two Asymmetric Players

Abstract

A contest is a situation in which players compete with one another by expending effort to win a prize. Examples abound. Firms compete by spending RD 26], Krueger [14], Posner [20], Rogerson [23], Appelbaum and Katz [1], Hillman and Riley [12], Hirshleifer [13], Ellingsen [8], Nitzan [18], and Baik [2; 3] have studied rent-seeking contests. Lazear and Rosen [15], O'Keeffe, Viscusi, and Zeckhauser [19], and Rosen [24] have examined performance incentives associated with reward schemes. Riley [22] has analyzed the war of attrition and auctions. Dixit [7] has considered strategic commitments in contests with different applications. These are only a part of the literature on the theory of contests. Despite the vast literature, however, the effects of asymmetries between players have not been clarified, except by Harris and Vickers [11] who analyze, in a patent race model, the strategic consequences of asymmetries. The purpose of this paper is to examine the effects of asymmetries between two players on individual and total effort levels in a model with a logit-form probability-of-winning function. Effort levels expended by the players deserve attention. Effort in a rent-seeking contest is interpreted as social costs and thus total effort level is a measure of economic efficiency; effort in an R&D contest is interpreted as R&D expenditures and thus effort levels determine the expected date of invention. We focus on asymmetries between the players resulting from their different valuations of the prize, their different abilities to convert effort into probability of winning, or both. Such asymmetries are common in contests. For example, people in different locations may receive different