Efficiency effects on coalition formation in contests

This paper studies the problem of endogenous coalition formation in contests: how players organize themselves in groups when faced with the common objective of securing a prize by exerting costly effort. The model presented adopts an axiomatic approach by assuming certain properties for the winning probability that imply efficiency gains from cooperation in contest settings. Efficiency gains are said to be generated if any coalition experiences increasing marginal returns with aggregate effort until a threshold. These properties identify a wide class of generalised Tullock contest success functions. We analyse a sequential coalition formation game for an arbitrary number of symmetric players and exogenous effort. If coalitions generate sufficient efficiency gains, then any equilibrium always consists of two or more coalitions where at least two coalitions are of unequal size. This result extends to endogenous efforts if the cost functions are sufficiently convex.