Sharing the Effort Costs in Group Contests

Abstract

This paper studies a contest among 2 groups for a public prize in which, by sharing the effort costs of the contest through transfer functions among players, groups mitigate the free rider problem. These problems arise because players in a group do not internalize the benefits that winning a public prize can yield to the group. How groups share the effort costs of the contest among their players is therefore analyzed. The transfer functions that mitigate the free rider problem are meritocratic, since induce players to exert more effort. When marginal costs are linear, the optimal transfer function is equivalent to split the effort costs of the contest in an egalitarian way. The case in which players within a group are heterogenoeus in the valuation of the public prize is analyzed. In such a case, players with lower valuations will be induced to exert effort through more meritocratic transfer functions than players with higher valuations. If transfer functions are restricted to be linear, the group chooses among a convex combination of two sharing rules: a rule in which every player assumes its own cost or the rule in which the effort costs of the contest are splitted in an egalitarian way. In case both groups have the same size, both groups split the effort costs of the contest in an egalitarian way. Otherwise, the larger group chooses an egalitarian rule while the smaller one chooses a mixed rule.