Rent-seeking contest when the prize increases with aggregate efforts

The objective of this article is to investigate contests in which efforts are productive. Tullock's standard rent-seeking model is extended by making the rent itself increase with the aggregate efforts. A positive externality is thereby introduced into the contest, because a contender's private effort in quest of the rent generates a benefit for other contenders. Coupled with a negative externality presented in the standard rent-seeking model, the net effect on the social efficiency of the contest is a priori ambiguous. It is shown that the extended contest generates socially wasteful, excessive aggregate efforts.     

On the limits to rent-seeking waste

The general equilibrium framework developed in this paper for analyzing the limits to rent-seeking waste goes beyond the existing literature by incorporating tax-financed, public subsidies and rent-protecting activities into a rent-seeking environment. We show that the limits to rent-seeking waste depend on the extent to which government subsidizes rent seekers and rent defenders through tax-financed grants, contracts and favors. As observed by Tullock (1967), the diversion of resources toward efforts to acquire a monopoly rent causes a social waste in addition to the excess burden of monopoly pricing measured by the Harberger triangle. In the absence of government subsidies to rent-seeking and under competitive conditions, this additional waste cannot exceed the maximum monopoly rent attainable. However, if government subsidizes expenditures on rent-seeking, then the additional waste can exceed the Tullock rectangle of monopoly rent and, in the limit, equal the economy's maximum potential social surplus.Rent avoidance expenditures reduce the rent to be captured and thus discourage rent-seeking. If rent avoidance is a relatively efficient mechanism for transferring consumer surplus to rent granters, then rent-seeking expenditures are displaced by less wasteful expenditures on rent defending. As a result, under competitive conditions, unsubsidized demand for private rent protection may be socially efficient. Nonetheless, the upper limit to rent-seeking waste depends on constitutionally determined maximum rates of public subsidies to rent-seeking and rent-avoidance activities.     

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.     

Privately informed seekers of an uncertain rent

Two departures from antecedent rent-seeking models are invoked: a rent of unknown size is sought, and rent seekers obtain private imperfect estimates of this size. A symmetric equilibrium for a fixed number of rent seekers is characterized, and shown to underdissipate the rent. Then a model of the decision to obtain private information and participate in the rent-seeking contest is built. The symmetric equilibrium participation probability equates expected profit to participation costs. A simple formula for underdissipation results: dissipation is incomplete precisely by the expected aggregate participation costs. If an award mechanism can attain a lower level of dissipation for a fixed number of seekers, then it will raise the endogenous probability of participation, and as a result will dissipate less rent in the equilibrium with an endogenous number of seekers.     

Risk aversion and rent-seeking: An extension and some experimental evidence

Theoretical investigations indicate that the risk attitudes of individuals will effect the amount of rent that can be assumed to be dissipated by rent-seeking activities. Following this line of investigation we extend Hillman and Katz's work to a small numbers case and demonstrate that the degree to which a monopoly rent is dissipated is dependent upon the structure of the risk attitudes of two risk averse individuals.Our earlier laboratory results were evaluated with respect to the risk neutral Cournot-Nash predictions. However, given the uncertainty present in the rent-seeking experiment, our ability to reject these risk neutral predictions may not be, in fact, a failure for the model but a result of risk aversion. In laboratory experiments in which we control for the relative risk attitudes of individual agents, we show that risk aversion matters. The relative risk aversion of individuals affects the level of rent-seeking activity and the extent to which rents are dissipated. In our experiments, the relatively less risk averse individuals dissipated relatively more rent.     

A generalized model of rent-seeking behavior

In this paper I present a formal analysis of rent-seeking games in which the players' valuations for the prize are represented as vectors. The players in this game are risk neutral and may not be indifferent to who wins the contestable rent if it is someone else. Both Tullock's original rent-seeking model and the public goods rent-seeking model by Katz et al. turn out to be special cases of this more general model.     

Stackelberg rent-seeking

In this paper I present a formal analysis of rent-seeking games in which the players do not move simultaneously. I consider rent-seeking situations where the players are risk neutral and may value the prize differently. The subgame perfect equilibrium outcome in this Stackelberg game provides several surprising and interesting results. I extend the problem to deal with cases of incomplete information concerning the value a player has for the politically contestable rent.     

寻租与反寻租:一个理论模型

本文试图对国内学术界偏好使用却又屡被误用的寻租理论作出学术澄清.本文认为,完整、准确的寻租理论应由如下四个命题组成:1.市场主体价值指向的租金非仅一种而是有三种,即分别由创新原因、自然原因和管制原因引致的垄断租金;2.市场主体追求创新租金的寻利行为是自由竞争条件下的正和博弈,而其追逐管制租金的寻租行为则是在不完全竞争条件下的负和博弈;3政府进行制度创新,引导市场主体从寻租走向寻利,可以实现反寻租的目的;4.由于政府同样具有理性经济人特征,通过制度创新进行反寻租有可能引起新的寻租,陷入反寻租的悖论.     

Rent-seeking with scarce talent: A model of preemptive hiring

In a standard rent-seeking contest, players optimally employ resources in an attempt to obtain the rent. Typically, it is assumed that these resources may be hired at any desired level at some exogenous per-unit cost. In practice, these resources often consist of scarce, talented individuals. We model a rent-seeking contest with scarce talent and find that talent scarcity leads to preemptive hiring by the player receiving the larger rent. This player hires all available talent and wins the contest with probability 1. This is true even when the difference in rents is small.     

Committees and Rent-Seeking Effort under Probabilistic Voting

Congleton (1984) shows that a rent awardedby a committee results in smaller aggregaterent-seeking expenditures than a similarrent awarded by a single administrator.This note modifies Congleton's model byconsidering a model in which voting isprobabilistic instead of deterministic. Ishow that the relative magnitudes ofrent-seeking expenditures could go eitherway depending on the relative weightedsensitivities (to rent-seeking efforts) ofthe committee and the single administrator.I show how the distribution of votingpowers of committee members affectsrent-seeking efforts. I also examine thecase where there is some probability thatthe rent may not be awarded, if thecommittee is unable to reach a majoritydecision. My results diverge from Congleton(1984) because of the absence ofmajoritarian cycles in my model.     

The design of rent-seeking competitions: Committees,preliminary and final contests

The paper examines the common practice in multi-contest rent- seeking competitions, where “finalists” are selected, based on rent-seekers' efforts in a preliminary contest. We find that for any single-contest design, rent-seeking expenditures could be reduced by introducing a preliminary contest, if the marginal returns to rent- seeking effort in the preliminary contest is sufficiently low. In addition to other reasons, the paper argues that this may explain why such multi-contest designs are common. We argue that rent-seeking expenditure in the preliminary stage represents the cost of reducing the number of contestants. We also find that the practice of setting a higher “quality” standard in the final contest than the “quality” standard in the preliminary contest reduces rent-seeking waste. We derive an expression for the optimal number of finalists; under certain conditions we find that the optimal number of finalists is directly proportional or equal to the square root of the number of potential contestants. Finally, we show that whether rent-seeking expenditures rise or fall when the rent is awarded by a committee instead of a single administrator depends on the sensitivity of the committee relative to that of the single administrator.     

Rent dissipation when rent seekers are budget constrained

In the original Tullock (1975, 1980) game, an individual bidder's probability of winning with a bid b is proportional to b^R, where the exponent reflects economies of scale in rent seeking. Different interpretations can be given to these probabilities. First, one may view R as a reflection of the political culture. Alternatively, one may view R as a choice variable for a politician. Intuition suggests that a society with a high tolerance for the selling of political favors and politicians who are receptive to rent seeking would both induce greater rent-seeking expenditures than other societies, all else equal. This paper shows that a lower value of R can actually lead to more rent dissipation than a higher value. This paper also reinforces two points concerning rent seeking. First, the analysis confirms the robustness of under-dissipation of rents, even in the face of entry. Second, it points out the importance of distinguishing between rent-seeking expenditures and rent dissipation. When bidders must borrow, for example, total expenditure may understate rent dissipation.     

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.     

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.     

The measurability of budget related rent-seeking

It has been suggested that the extent of rent-seeking expenditures arising from attempts to influence budget allocations should be estimated by the absolute magnitude of the observed changes in allocation. Instead, we argue that it is the extent of theex ante prospective changes that determine the level of rent-seeking, and that in the presence of countervailing activity these may be quite unrelated to the ex post observed values. We further argue that the traditional rent-seeking model of competition for a pre-specified rent is inappropriate in this context.     

Political instability in Africa: A rent-seeking approach

The foregoing analysis developed the paradigm of self-interest motivated revolutionary activities. In effect, the construct presented differs from the by-product theory developed by Tullock only in its specific modeling of government-created rents as the engine which drives the violent political behavior. The empirical test of the positive relationship between rent creation by the government and the amount of destabilizing political activity yields strong support for the structuring of politically destabilizing activities as rent-seeking in nature. It is the authors' hope that further empirical investigation and a more general and rigorous modeling of revolution as a rent-seeking activity will become an important part of the literature in public choice.Finally, some policy implications should be discussed. The policy emphasis for the governments of Africa countries should be on opening the economy to competition. Instituting programs to make the economic system more accessible to all segments of society would result in reduced opportunities for rent-seeking. Reducing rent-seeking should result in increased political stability. A reduction in government market intervention would also reduce the costs of government regulations on individual entrepreneurs inducing them to increase their participation in economically productive activities. Taken together the result would be increased political stability and higher rates of economic growth.     

Rent-seeking behaviour of retaliating agents

This paper has examined a rent-seeking game where the players take a more sophisticated approach to evaluating the potential strategies and counter-strategies of their rivals than in the standard Nash case. We have derived the conditions for the existence of symmetric and nonsymmetric equilibria for the game and derived the properties of these equilibria. Three results merit repeating. First, we find that rent dissipation will not, in general, be complete. Second, and in contrast to much of the traditional literature, we find that the socially optimal result of zero rent-seeking is sometimes a feasible equilibrium outcome for our game. Finally, there exist rent-seeking configurations in which the best play of one of the rivals is to withdraw from the game or, alternatively stated, where it is not optimal for a rival to contest the rent by entering the game. In these nonsymmetric cases it would appear that Tullock's conjecture about the value of preemptive moves remains valid. This is true even when the strategies and counter-strategies available to the players are much more complex than in the traditional Nash approach.As a final point we raise the issue of whether or not it is reasonable to suppose that the players in rent-seeking games will take their strategy and counter-strategy sets to be as large as we have assumed in this paper. Players may well make their moves and counter-moves based upon rules of thumb or other considerations that effectively bound the strategy sets of the players. As well, it may be useful to consider games where players, upon entering the game, commit themselves to a given level of expenditures. Many of these issues are considered in a related paper by the authors.     

Contests with an unknown number of contestants

This paper studies rent-seeking contests where the contestants do not know the number of actively competing contestants. Two models are compared. In the first, all players are risk neutral; in the second, all have constant absolute risk aversion. If the expected fraction of active contestants is low, an increase in the number of potential contestants increases individual rent-seeking efforts. This effect is in contrast to the complete information case where individual rent-seeking efforts decrease in the number of contestants. The effect is more likely under risk neutrality, but also possible under risk aversion. Equilibrium rent seeking efforts are lower under risk aversion if and only if the expected fraction of active contestants is low.     

Rents, dissipation and lost treasures: Rethinking Tullock's paradox

In this paper we revisit Tullock's paradox (Tullock, 1980) and consider a rent-seeking game in which parties face increasing returns to effort. We allow parties to randomize their strategies and give them an exit option. Given the mixed participation strategies of the parties, valuable rents may occasionally remain unexploited. We consider such a lost-treasure effect as an additional cost of rent seeking and examine how the expected value of such a lost rent varies with changes in the parameters of the problem.     

Efforts in two-sided contests

The degree of rent dissipation is studied in extended two-sided contests that involve two types of efforts. While usual contestants expend resources in trying to win the contested prize, potential recipients of the rent-seeking efforts also participate in the contest. This is due to uncertainty regarding the source of power in the contest that induces the bureaucrats to expend resources to increase their share in the rent-seeking efforts by trying to appear as the party controlling the allocation of the prize. We show that the existing theoretical and empirical studies are incomplete and may underestimate the extent of rent dissipation.