Rent seeking and rent dissipation: A neutrality result

We consider rent seeking contests between at least two agents who might value the prize differently. We capture a wide range of institutional aspects of contests by analyzing a class of contest success functions fulfilling several properties. The main properties are anonymity and a condition on the elasticity of a rent seeker's win probability with respect to her effort. We show the existence of a mixed-strategy equilibrium and establish equilibrium payoffs. In this equilibrium complete rent dissipation holds. Our results imply a partial robustness result for the all-pay auction.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

Group competition for rents

This paper examines rent dissipation in a two-stage group rent-seeking contest without a predetermined distribution rule. the rent in this setting exhibits both public and private good characteristics depending on the stage of the contest. Focusing on the relationship between group size and aggregate rent seeking we find that social waste depends not only on total numbers but also on the distribution of population across groups. We show that group size asymmetry acts to reduce rent dissipation.     

Rent Seeking with Politically Contestable Rights to Tariff‐rate Import Quotas**

This paper analyzes rent seeking for agricultural import quotas and the associated waste of resources when politically contestable licenses are allocated to either or both importers and exporters. In a two‐stage simultaneous contest where firms seek rent for licenses and then bargain over the import/export price, it is shown that (1) rents are not dissipated completely because of uncertainty in allocation of “rights,” (2) the dissipation ratio increases if the country with a more competitive contest increases the probability of establishing licenses, (3) rent seeking may cause the market structure to change, (4) less rent is dissipated in the case of pre‐existing market power, and (5) allocation of multiple licenses decreases rent‐seeking outlays.     

When less is more: Rationing and rent dissipation in stochastic contests

This paper shows how to maximize revenue when a contest is noisy. We consider a case where two or more contestants bid for a prize in a stochastic contest where all bidders value the prize equally. We show that, whenever a Tullock contest yields under-dissipation, the auctioneer?s revenue can be increased by optimally fixing the number of tickets. In particular, in a stochastic contest with proportional probabilities, it is possible to obtain (almost) full rent dissipation. We test this hypothesis with a laboratory experiment. The results indicate that, as predicted, revenue is significantly higher in a lottery with rationing than in a standard lottery. On the other hand, an alternative rationing mechanism that does not limit total expenditures fails to increase revenue relative to a standard lottery.     

Multi-activity contests

In many contests, players can influence their chances of winning through multiple activities or “arms”. We develop a model of multi-armed contests and axiomatize its contest success function. We then analyze the outcomes of the multi-armed contest and the effects of allowing or restricting arms. Restricting an arm increases total effort directed to other arms if and only if restricting the arm balances the contest. Restricting an arm tends to reduce rent dissipation because it reduces the discriminatory power of the contest. But it also tends to increase rent dissipation if it balances the contest. Less rent is dissipated if an arm is restricted as long as no player is excessively stronger than the other with that arm. If players are sufficiently symmetric in an arm, both players are better off if that arm is restricted. Nevertheless, players cannot agree to restrict the arm if their costs of using the arm are sufficiently low.     

WINNER-HELP-LOSER GROUP FORMATION IN RENT-SEEKING CONTESTS*

We define a winner-help-loser group in a rent-seeking contest as follows: (a) the member players compete noncooperatively to win the rent, and (b) if a member player wins the rent, he helps the losing member players according to the previously written agreement. We demonstrate that one and only one winner-help-loser group is formed voluntarily. One important consequence of such group formation is that rent dissipation is small relative to individual rent seeking. Therefore, such group formation decreases the social cost associated with rent seeking and thus decreases the economic inefficiency of rent seeking.     

On the Existence and Uniqueness of Pure-Strategy Nash Equilibrium in Asymmetric Rent-Seeking Contests

There can be three types of heterogeneity among players in a rent‐seeking contest. First, effectiveness of player's effort on the winning probabilities may differ among players. Secondly, players may evaluate the rent or prize of the rent‐seeking contest differently. Thirdly, players may face different financial constraints. This article proves under standard assumptions in the literature that there exists a unique pure‐strategy Nash equilibrium in a general asymmetric rent‐seeking contest with these three types of heterogeneity among players.     

Rent Seeking and Allocative Efficiency

This paper considers a rent‐seeking game (specifically, a winner‐takes‐all contest) with incomplete information. By allowing for sequential moves, a Bayesian‐Stackelberg equilibrium can be constructed. It can be shown that, at the Bayesian‐Stackelberg equilibrium, it is always possible that the allocative efficiency argument fails. That is, there are cases in which the Stackelberg follower is more efficient but loses the contest. Using a specific class of distributions, it is also shown that sometimes the corrupt official will choose the Bayesian‐Stackelberg equilibrium over the Bayesian‐Nash equilibrium in order to maximise the expected bribe revenue. That is, when designing the rules of the rent‐seeking game, the dynamic nature of competition will be taken into account.     

Round‐Robin Tournaments with a Dominant Player

We analyze the subgame perfect equilibrium of the round‐robin tournament with one strong (dominant) and two weak players, and we compare this tournament and the one‐stage contest with respect to the players' expected payoffs, expected total effort, and their probabilities of winning. We find that if the contest designer's goal is to maximize the players' expected total effort, then – if the asymmetry between the players is relatively low – the one‐stage contest should be used. However, if the asymmetry is relatively high, then the round‐robin tournament should be used.     

Risk aversion in symmetric and asymmetric contests

We analyze existence, uniqueness and properties of equilibria in incompletely discriminating Tullock contests with logistic contest success functions, when contestants are risk averse. We prove that a Nash equilibrium for such a contest exists, but give an example of a symmetric contest with both symmetric and asymmetric equilibria, showing that risk aversion may lead to multiple equilibria. Symmetric contests have unique symmetric equilibria but additional conditions are necessary for general uniqueness. We also study the effects on incumbents of additional competitors entering the contest under these conditions and examine the effects of risk aversion on rent dissipation in symmetric and asymmetric contests.     

The best-shot all-pay (group) auction with complete information

We analyze an all-pay group contest in which individual members’ efforts are aggregated via the best-shot technology and the prize is a public good for the winning group. The interplay of within-group free-riding and across-group competition allows for a wide variety of equilibria, according to how well groups overcome internal free-riding. In contrast with the existing literature, we derive equilibria of a symmetric model in which multiple agents per group are active. Our findings differ qualitatively from those of the individualistic all-pay auction: rents are not necessarily dissipated in equilibrium, total expected efforts vary across equilibria, and participation is expected to be greater. Moreover, equilibria with greater symmetry of behavior within a group are shown to have more “wasted” effort but also greater payoffs as overall efforts are lower. In contrast to standard economic intuition, free-riding can be beneficial for players as it reduces competition among groups. Examples of asymmetric group contests are also studied.     

Information feedback and contest structure in rent-seeking games

We investigate the effects of information feedback in rent-seeking games with two different contest structures. In the share contest a contestant receives a share of the rent equal to her share of rent-seeking expenditures, while in the lottery contest a contestant wins the entire rent with probability equal to her share of rent-seeking expenditures. In share contests average expenditures converge to equilibrium levels when subjects only get feedback about own earnings, and additional feedback about rivals' choices and earnings raises average expenditures. In lottery contests information feedback has an opposite, and even stronger, effect: when subjects only get feedback on own earnings we observe high levels of rent dissipation, usually exceeding the value of the rent, and additional feedback about rivals' choices and earnings has a significant moderating influence on expenditures. In a follow-up treatment we make information feedback endogenous by allowing contestants in a lottery contest to make public or private expenditures. Subjects make the vast majority of expenditures privately and overall excess expenditures are similar to the lottery contest with own feedback.     

Rent, risk, and replication: Preference adaptation in winner-take-all markets

We study the evolution of an economy where agents who are heterogeneous with respect to risk attitudes can either earn a certain income or enter a risky rent-seeking contest. We assume that agents behave rationally given their preferences, but that the population distribution of preferences evolves over time in response to material payoffs. We show that, in particular, initial distributions with full support converge to stationary states where all types are still present. Although rents are perfectly dissipated in material terms at a steady state, efficiency is greater than if everybody had been risk neutral, since risk lovers specialize in rent seeking.     

Exit from Rent‐Seeking Contests

The object of this paper is to investigate the long‐run behaviour of rent‐seekers in a situation where they incur negative expected payoffs due to increasing returns to rent‐seeking expenditures. To this end, we embed the one‐shot rent‐seeking game presented by Tullock (1980) in the war‐of‐attrition framework. In this multi‐period setting, each player not only determines his or her rent‐seeking expenditure but also chooses a mixed strategy on whether to stay in or exit from rent‐seeking competition in each period. JEL Classification Numbers: D72, C72, L12     

LOBBYING CONTESTS WITH ENDOGENOUS POLICY PROPOSALS

Lobbyists choose what to lobby for. If they can precommit to certain policy proposals, their choice will have an influence on the behavior of opposing lobbyists. Hence lobbyists have an incentive to moderate their policy proposals in order to reduce the intensity of the lobbying contest. This logic has been explored in a number of recent papers. I reconsider the topic with a perfectly discriminating contest. With endogenous policy proposals, there is a subgame-perfect equilibrium where the proposals of the lobbyists coincide and maximize joint welfare; moreover, this equilibrium is the only one that survives repeated elimination of dominated strategies. Hence there is no rent dissipation at all. A politician trying to maximize lobbying expenditures would prefer an imperfectly discriminating contest.     

Effort and performance in group contests

We study contest performance by focusing on the per capita payoffs of the contestants in an important class of asymmetric two-group contests. The group with the higher valuation has a greater chance of winning the contest whenever the rent-seeking technology is increasing and concave. We note that equilibrium efforts and payoffs per capita are uniquely defined and can be subjected to a comparative statics analysis. We show that payoff per capita for a group increases with its own valuation but decreases with the valuation of the opposing group. Per capita payoff for a group increases with its population.     

Corporate Social Responsibility and International Competition: A Welfare Analysis

This paper examines the welfare implications of corporate social responsibility (CSR) in international markets under imperfect competition. Based on a stylized model of an import‐competing duopolistic market, we show the feasibility of moving toward tariff reductions when both domestic and foreign firms launch CSR initiatives in that their payoffs include not only individual profits, but also the benefits of consumers. For the case where the foreign exporter unilaterally adopts the consumer‐oriented CSR as a strategy, there is a rent‐shifting effect because the foreign firm's payoff increases whereas the domestic firm's profit decreases. In response, the importing country's government raises its tariff on the foreign product. If, instead, the domestic firm adopts the CSR strategy unilaterally, the rent‐shifting effect disappears and both the competing firms’ payoffs increase. We further identify the conditions under which the CSR initiatives of the firms constitute the dominant strategy, leading to a Pareto efficient outcome at which the firms’ payoffs, consumer surplus, and social welfare are at their maximum levels.     

Are sequential round‐robin tournaments discriminatory?

I examine sequential round‐robin tournaments with three and four symmetric players. Each player is matched once with each other player and each match is organized as a Tullock contest. A single prize is allocated to the player with the most matches won. I show that, depending on the position of their matches in the sequence of the tournament, the players' ex ante winning probabilities and expected payoffs differ. Compared to tournaments with matches organized as all‐pay auctions, however, discrimination is weaker and partially reversed. Moreover, aggregate effort in tournaments with suitable Tullock contests is larger than in tournaments with all‐pay auctions. The fairness of round‐robin tournaments may be improved by an endogenous sequence of matches or the requirement that players fix their effort ex ante.     

Contests where there is variation in the marginal productivity of effort

Summary. We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function, that output is increasing in ability, and that marginal effort is increasing in ability, while effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win, with independently distributed abilities. We analyze the contest designer's decisions in choosing contest rules optimal from her perspective. We show that the output produced, probability of winning, and contest designer's expected revenue are generally increasing in contestants' ability. We examine the relationship between the marginal cost of producing output and marginal utility per dollar of the net award for winning. Received: July 30, 1998; revised version: August 7, 2000