Equilibrium Conditions for Efficient Rent Seeking: The Nash-Cournot Solution
Tullock presents a model of the rent-seeking behavior of risk-neutral individuals. This model has sparked the interest of a number of researchers1 and the literature has expanded Tullock’s model in a variety of directions. This article sets out the original problem in the formal framework of a Nash-Cournot game. While only part of Tullock’s original article looks at rent seeking in the Nash-Cournot framework, this framework is a useful way to summarize the analysis of rent-seeking behavior. I will show that many of the problems addressed by other authors can be seen more clearly when one works through the detailed results of Tullock’s model using the Nash-Cournot equilibrium concept.2 I will also show the pedagogical value of using this unifying framework to study rent-seeking behavior, and I will present an important result concerning the possibility of overdissipation as stated in Tullock’s original model.
KeywordsExpected Profit Rent Seeker Cournot Equilibrium Monopoly Rent Marginal Cost Curve
Unable to display preview. Download preview PDF.
- I would like to thank Joseph Jadlow, David Schap, Gordon Tullock, and a referee from The Quarterly Review of Economics and Business for helpful comments on this topic.Google Scholar
- 1.See Corcoran , Corcoran and Karels , Higgins, Shughart, and Tollison , Hillman and Katz , Jadow , Rogerson , and Tullock [9, 10] for various specifications of the model. For an alternative model, which argues that rents may be dissipated in the form of nonprice competition, see Gifford .Google Scholar
- 2.Other game theoretic solutions to the rent-seeking problem can be found in those articles cited in note 1. While some of these formulations extend outside of the Nash-Cournot equilibrium framework, they all begin their modeling by using the Nash-Cournot solution as the point of departure.Google Scholar
- 3.Tullock , p. 97, reports that the second-order conditions are not met when R N/(N— 2). His statement is incorrect, and the inequality should be reversed.Google Scholar
- 4.Corcoran  and Corcoran and Karels  attempt to rationalize a similar result based on a zero expected profit condition that is driven by entry and exit. The result obtained here is independent of the number of rent seekers and depends only on a rational participation rule for risk-neutral individuals.Google Scholar
- 5.These results can be derived directly from partial differentiation of the equation C = R(N-1)1 N. Holding N fixed, C increases with Rat a fixed rate equal to (N-1) IN. Holding R fixed, C increases with Nat a decreasing rate. The cross partial is positive.Google Scholar
- 6.The solutions proposed by Corcoran and Karels  to obtain a rent-seeking ratio equal to + 1, such as bet splitting and so-called preemptory betting, depend on strategic behavior on the part of individuals and, thus, do not fit into the Nash-Cournot equilibrium framework.Google Scholar
- 7.Whether these secondary rent-seeking costs are observed depends on whether the incumbents in the primary rent-seeking competition actually sell their “participation rights” or simply treat the value of those rights as an opportunity cost of remaining in the primary rent-seeking competition.Google Scholar