A multi-winner nested rent-seeking contest

Public Choice - This paper considers a symmetric imperfectly discriminating rent-seeking contest in which there may be several winners. We first demonstrate a serious flaw in previous work and then...     

Delegation with multiple instruments in a rent-seeking contest

We consider delegation in a rent-seeking contest with two players, where delegates have more instruments at their disposal than the main players. We endogenize both the decision to hire a delegate and the contingent fee offered to the delegates. We characterize the situations when either no, one or two players hire a delegate in equilibrium. We show that the decision to hire a delegate depends in a non-monotonic way on the size of the contested prize.     

Tullock's rent-seeking contest with a minimum expenditure requirement

We consider a rent-seeking contest of the kind introduced by Tullock (1980) in which two players compete for a monopoly rent. We extend the contest by requiring that if a player puts forward an effort, his expenditures must be larger than or equal to some minimum level. We show that, depending on the model parameters, the number of Nash equilibria of the extended model can be zero, one, two or four. Furthermore, it turns out that the extent of rent dissipation in a Nash equilibrium of the extended model can be larger than, equal to, or smaller than the extent of rent dissipation in the unique Nash equilibrium of the original model.     

Activity and inactivity in a rent-seeking contest with private information

We consider a rent-seeking contest in which one player has private information about his own valuation of the prize. This valuation may be either high or low. All other players have a known and identical valuation of the prize. We present necessary and sufficient conditions under which the privately informed player exerts a positive or zero equilibrium effort.     

Price discrimination in a rent-seeking economy

This paper examines the incentive and the consequences of using discriminatory pricing by a monopolist in a rent-seeking economy. It is shown that, even if all consumer groups' demands have identical elasticities at any given price, the monopolist has an incentive to charge a lower price to high pressure consumer groups so as to alleviate their rent-seeking efforts in challenging its monopolistic power. Furthermore, it is shown that by allowing the firm to price discriminate total welfare may increase, even if all rent-seeking expenditures are completely wasteful.     

Corporate political offices in a rent-seeking society

This paper examines agent discretion that is a result of the structure of the legislative process. Based on several distributions of lawmaking powers, different games are analyzed in which players decide on regulatory policies. The analysis shows that agent discretion increases as lawmaking powers are differentiated and assigned to specialized players. Particularly, monopoly initiation power, which allows a player to act as a gatekeeper, has a substantial impact on discretion. Agent discretion will be even larger when these players also have heterogenous preferences. The framework that is developed in this paper permits comparisons across different political systems with regard to agent discretion and legislative control on policymaking.     

Legal expenditure as a rent-seeking game

Legal expenditures at a civil trial constitute an interesting type of rent-seeking contest. In civil litigation there is a natural interaction between the objective merits of the case and the outcome of the contest. Institutions such as fee shifting do not generally have a counterpart in other rent-seeking contests. The endogenous decision to participate in the rent-seeking contest corresponds to the decision by the plaintiff to bring a case, and the decision by the defendant to defend it. The desirability of fee shifting is very sensitive to the value of the parameter which describes the legal technology.     

Risk aversion in two-period rent-seeking games

This work analyzes a two-period rent-seeking game, with the aim of studying the effect of risk aversion on the optimal choices made by the rent-seekers. We first prove that the equilibrium in two-period rent-seeking games always is unique. The analysis also shows that more risk aversion reduces the investment in the rent-seeking game in a two-period framework without introducing the additional condition of prudence, required in one-period models. Similarly, the introduction of a risky rent, instead of a given rent, implies, in the two-period framework, a reduction in investment under the condition that the rent-seekers are risk averse. Moreover, with risk aversion, larger first-period wealth increases investment in the rent-seeking game and larger second-period wealth reduces it. When both first-period and second-period wealth increase, investment in the rent-seeking game declines if the rent-seeker is risk averse and imprudent. Lastly, when a risky level of second-period wealth is introduced, the rent-seeker increases (reduces) investment in the rent-seeking game if he is risk averse and prudent (imprudent).

     

Endogenous sharing rules in collective-group rent-seeking

This paper examines the possibility of endogenous determination of intra-group sharing rules in a collective-group rent-seeking game. Collective-group rent-seeking is considered as a two-stage Nash-Cournot game in which sharing rules are determined prior to individual decision on voluntary contribution. The solution is subgame perfect and is obtained by backward induction. In competition between two groups of the same size, the Nash equilibrium sharing rule of each group is to distribute rent to each according to relative effort. Total rent-seeking outlays in this case are equal to those obtained by Tullock (1980). When more than two groups compete for a rent, the sharing rule based on relative effort is again likely to be the Nash equilibrium strategy of each group. The amount of total rent-seeking outlays is also equal to that in Tullock (1980). In a nutshell, the rent is substantially dissipated if sharing rules are endogenously determined.     

Learning the structure of a simple rent-seeking game

This paper considers a form of the Tullock imperfectly discriminating rent-seeking game in which the contestants are uncertain about the value of a bias parameter in the probability of winning function. Beliefs about this unknown parameter are not constrained to be static; we consider two methods by which the players' prior beliefs on this parameter can be updated. First, we allow for information to emerge by considering the case in which the game is played twice, with the outcome of the first game known before the second begins. The identity of the winner of the first contest represents information which emerges endogenously that can be used to revise beliefs on the unknown bias parameter. Second, information can be produced outside of the model by an external agency; this gives rise to exogenous learning. We consider the consequences for rent-seeking in each of these two cases.     

Crowding-out in productive and redistributive rent-seeking

This paper presents a general rent-seeking model in which participants decide on entry before choosing their levels of efforts. The conventional wisdom in the rent-seeking literature suggests that the rent dissipation increases with the number of potential participants and with their productivity of effort. In this paper, we show that this result of the rent-seeking literature is far from general and applies only when participants are relatively weak and enter the game with certainty. In the presence of strong competitors, the expected total dissipation actually decreases, since participation in the game is less frequent. We further consider the impact of competitors’ exit option, distinguishing between “redistributive rent-seeking” and “productive rent-seeking” situations. In redistributive rent-seeking, no social loss results from the fact that all competitors exit the race. In productive rent-seeking, instead, lack of participation creates a social loss (the “lost treasure” effect), since valuable rents are left unexploited. We show that the lost-treasure effect perfectly counterbalances the reduction in rent dissipation due to competitors’ exit. Hence, unlike redistributive rent-seeking, in productive rent-seeking the total social loss remains equal to the entire rent even when parties grow stronger or the number of players increases.     

Returns to effort in rent-seeking games

In the traditional formulation of rent-seeking games, increasing returns to effort are characterized by an exponent r>1. However, when the value of the rent is normalized to 1, the players’ effort levels A and B will typically be less than 1. Thus, when A<1 and r>1, the value of A ^r decreases as r increases, contradicting the interpretation of r>1 as representing increasing returns to effort. This apparent defect in the mathematization of the problem seems to suggest that a different interpretation of r is required whenever A<1, upsetting the uniformity and elegance of the model. In this short note, we demonstrate that the perceived problem is illusory, and that the usual interpretation of r is satisfactory for all values of A.     

Risk-aversion and prudence in rent-seeking games

This paper considers a common n-agent symmetric rent-seeking game. It derives conditions so that risk-aversion and risk always decrease rent-seeking efforts. These conditions hold for any regular contest success function when risk-averse rent-seekers are also prudent. Under n=2, prudence is a necessary and sufficient condition for risk-aversion to decrease rent-seeking efforts compared to risk-neutrality. An intuition for this result is given based on a self-protection model.     

Reexamining efficient rent-seeking in laboratory markets

Given Millner and Pratt's (1989) finding of behavior inconsistent with theory, we reexamine efficient rent-seeking in experimental markets. We show that (a) when r = 3, no Nash equilibrium exists and therefore behavior has no theoretical benchmark to judge consistency, and (b) when r = 1, with a new experimental design utilizing an explicit expected payoff matrix, rent-seeking behavior is consistent with both Nash equilibrium and dissipation hypotheses.The authors gratefully acknowledge the financial support of The John A. Walker College of Business, Appalachian State University. Cliff Nowell provided generous advice. John Willingham supplied valuable research assistance. Michael Pratt and Gordon Tullock provided helpful comments on an earlier version of the paper.     

Competitive-share group formation in rent-seeking contests

We examine the possibility of forming a competitive-share group in rent-seeking contests. The competitive-share group has the following characteristics: (a) the group is treated as a single player competing with the nonmembers to win the rent, (b) the members choose their outlays noncooperatively, and (c) the members compete to take larger shares of the rent. We show that the competitive-share group is always formed voluntarily. One important consequence of such group formation is that rent dissipation is less relative to individual rent seeking — in other words, the social cost associated with rent seeking is less.     

The incidence of overdissipation in rent-seeking contests

Tullock's analysis of rent seeking and overdissipation is reconsidered. We show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players' mixed strategies the total amount spent competing for rents can exceed the value of the prize. We also show that the cross-sectional incidence of overdissipation in the perfectly discriminating contest ranges from 0.50 to 0.44 as the number of players increases from two to infinity. Thus, even though the original analysis of overdissipation is flawed, there are instances in which rent-seekers spend more than the prize is worth.