The solution to the Tullock rent-seeking game when R > 2: Mixed-strategy equilibria and mean dissipation rates

Abstract

Abstract. In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium, exists when R > 2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.

Contests with a stochastic number of players

“…This intuition is similar to the idea behind Baye, et al (1994Baye, et al ( , 1999 who show that ex-post over-dissipation can take place as a particular realization of a mixed-strategy equilibrium. We summarize this subsection with the following theorem.…”

“…For example, in many rent-seeking contests an individual lobbyist does not know how many other lobbyists are competing for the rent when she exerts her effort. 3 In this paper, we consider Tullock's n-player contest where each player has an independent probability 0 < p ≤ 1 of participation.…”

“…Hillman and Samet (1987) and Baye, et al (1994Baye, et al ( , 1999 show that ex-post over-dissipation can take place as a particular realization of a mixed-strategy equilibrium. We demonstrate that ex-post over-dissipation is a natural feature of the pure-strategy equilibrium if the number of players is stochastic.…”

Conflicts with Multiple Battlefields

“…First, it is obvious that other contest success functions may be applied within battlefields such as the Tullock contest success functions with exponent greater than two, 18 Lazear and Rosen's (1981) difference-form contest success functions, 19 Konrad's (2002) treatment of 18 In the case of a single contest, partial characterizations of equilibrium for this model for discrete approximations to a continuous strategy space have been derived by Baye et al (1994) and Alcalde and Dahm (2010). 19 Previous analyses of the Lazear-Rosen (1981) difference-form contest success function for single contests affine handicapping in the context of the auction CSF, or Skaperdas and Syropoulos's (1998) treatment of weighted asymmetric lottery CSFs.…”

Rents, dissipation and lost treasures: Comment

“…1 They introduce an exit option and propose a mixed strategy equilibrium for the case of increasing returns in the contest success function (r > 2): Each player mixes between two strategies: nonparticipation, and participation with one uniquely de…ned positive level of investment in rent-seeking activities.…”