Advantageous multiple rent seeking

Abstract

This paper analyzes a special rent seeking game which has not been studied in the literature on pressure groups competition, rent seeking, lobbying or auctions. We consider a multiple rent contest where n identical allocators (players) with constrained resources compete under full information over a fixed supply of m (2⩽ m< n) advantageous rents (prizes). Pure strategy Nash equilibria exist in this game. Symmetric mixed strategy Nash equilibria (SMSEs), however, may not exist. A general existence condition for SMSEs is provided. When n is sufficiently large, SMSEs always exist. Assuming that the rents are identical we derive a necessary and sufficient condition (in terms of the relationship between n and m) for the existence of a unique SMSE. We also provide the characterization of the equilibrium allocation of the constrained resources of the players among the homogeneous or heterogeneous rents. It turns out that, in equilibrium, interest group leaders always concentrate their resources in attempting to secure just one of the political benefits. The distribution of allocators over the political favors (prizes) they wish to win almost reveals the relative values of the prizes.