Prize-allocation rules in generalized team contests

We consider a generalized team contest, in which the team’s effort is produced with a general technology represented by a concave homothetic function of team members’ contributions. Furthermore, we assume that the value of the contest’s prize depends on total effort exerted in the contest. We prove the existence of positive-effort Nash equilibrium for this generalized team contest under an arbitrary profile of the teams’ prize-allocation rules, and derive a simple characterization of the team-effort-maximizing prize-sharing rule. Although our basic model assumes that each individual in a group has constant marginal effort costs, it is possible to extend the results to the case where team members’ effort cost functions have increasing marginal costs with a constant elasticity.