Contests with group-specific public goods and complementarities in efforts

Abstract

This paper starts from the observation that in public-goods group contests, group impact can in general not be additively decomposed into some sum (of functions) of individual efforts. We use a CES-impact function to identify the main channels of influence of the elasticity of substitution on the behavior in and the outcome of such a contest. We characterize the Nash equilibria of this game and carry out comparative-static exercises with respect to the elasticity of substitution among group members’ efforts. If groups are homogeneous (i.e. all group members have the same valuation and efficiency within the group), the elasticity of substitution has no effect on the equilibrium. For heterogeneous groups, the higher the complementarity of efforts of that group, the lower the divergence of efforts among group members and the lower the winning probability of that group. This contradicts the common intuition that groups can improve their performance by solving the free-rider problem via higher degrees of complementarity of efforts.