We examine the strategic behavior in joint production within a partnership in the context of a contest with an endogenous prize, and we explore the optimal choice of the sharing rule and its effect on the dispersion of rewards. We prove the existence and uniqueness of the pure strategy Nash equilibrium under no participation constraints for a large class of production functions and sharing rules, and obtain an explicit solution for the symmetric case. For the asymmetric case, we undergo numerical simulations for both utilitarian and Rawlsian partnership. Our results illustrate how the partnership compensation depends on the relative productivity of the players, the economies of scale and the substitution (complementarity) of the efforts in the joint production.
Wang et al. (Wed,) studied this question.