Rent-seeking with asymmetric valuations: Addition or deletion of a player

We consider an extension of Tullock's (1980) N-player contest under which prize valuations may vary across players. We show that the pure-strategy equilibrium of this contest is unique. We also establish the following results: rent dissipation increases, individual winning probabilities decrease, and individual spending either increases or decreases with the addition of a player.     

Learning by doing in contests

We introduce learning by doing in a dynamic contest. Contestants compete in an early round and can use the experience gained to reduce effort cost in a subsequent contest. A contest designer can decide how much of the prize mass to distribute in the early contest and how much to leave for the later one in order to maximize total efforts. We show how this division affects effort at each stage, and present conditions that characterize the optimal split. There is a trade off here, since a large early prize increases first period efforts leading to a substantial reduction in second round effort cost; on the other hand, there is less of the prize mass to fight over in the second round, reducing effort at that stage. The results are indicative of the fact that the designer often prefers to leave most of the prize mass for the second contest to reap the gains from the learning by doing effect.     

Experimental comparison of two multiple-stage contest designs with asymmetric players

We compare experimentally two contest designs. In the between-group design (BGD), cohorts compete with one another in stage 1 and a single cohort is then advance to stage 2. In stage 2, members of this cohort compete for a single prize. In the within-group design (WGD), the order of the competition is reversed. Our findings support the theoretical conclusion that the WGD is superior to BGD in generating more expenditure. They also show that if the cohorts are fixed, small, and interact repeatedly over time, then tacit collusion in the WGD, but not the BGD, leads to suppression of expenditures.     

Performance and prize decomposition in contests

This paper focuses on the effect of additive contest decomposition on performance: winning probabilities and efforts of the contestants. Our main result provides a sufficient condition for invariance of contest performance to the decomposition of a contest, when the sum of the possibly differently valued prizes in the segmented contests is equal to the value of the prize in the original grand contest and the relative prizes in the sub-contests are equal for every contestant. It is shown that this condition is satisfied by the commonly used exponential logistic contest success functions. With these functions the contest designer does not have an incentive to split the prize and create additive, segmented sub-contests. We then prove that when the additive contest decomposition is asymmetric, contest decomposition may adversely affect the designer; that it, reduce the total efforts of the contestants.     

Varying the intensity of competition in a multiple prize rent seeking experiment

We experimentally test a rent seeking model under five levels of competition. At one extreme, a subject’s probability of winning a prize is equal to her share of the total expenditures. At lower levels of competition, a subject’s probability of winning is affected more by her own expenditures than by the expenditures of others. Predicted expenditure levels are positively associated with higher levels of competition. Consistent with previous rent seeking experiments, we find that subjects spend significantly more than the Nash equilibrium prediction at all levels of competition. However, expenditure patterns generally follow the Nash prediction; expenditures decrease as the level of competition decreases. Our experimental design also includes a lottery choice experiment to control for subjects’ risk preference. We find that subjects who are more risk averse spend significantly less in the contest and this effect is particularly strong for female subjects.     

Optimal contest design, closeness and the contest success function

This paper considers the optimal design of an asymmetric two-player contest when the designer’s payoff depends not only on performance of the contestants, but also on the closeness of the contest measured by the difference in winning probabilities. In contrast to previous studies, the impact of closeness on the optimal prize depends on the shape of the contest success function. Furthermore, including closeness in the designer’s objective may induce the designer to uniformly increase the contestants’ effort costs. A similar result is obtained in case the designer may handicap the stronger contestant, but an even contest is never optimal.     

Sent Seeking With Private Values

We study a rent-seeking contest in which the players'valuations of the prize are private information. We determinea Bayesian equilibrium and give conditions under which theequilibrium exists. Although players are ex ante symmetric,increased possibilities for ex post lopsidedness lead toless aggressive bidding. (Lopsidedness increases as players'values become less positively correlated or as the variationin possible values increases.) We also compare theprivate-information contest to a related public-informationcontest in which the realizations of values are commonknowledge. The contests are equally efficient and players areindifferent between the two, but risk-averse sellers of theprize are not.     

Two-Stage Rent-Seeking Contests with Carryovers

We examine a two-stage contest in which players in twogroups compete noncooperatively to win a rent. In thefirst stage, each group selects a finalist. The twofinalists compete for the rent in the second stage.First-stage efforts are carried over to the secondstage in the sense that they are partly effective inthe second stage as well. We show the following. Inthe case of player-specific carryovers, therent-dissipation rate increases in the carryover rate.With the carryover rate equal to one, the rent isfully dissipated. In the case of group-specificcarryovers, however, the rent-dissipation rate isindependent of the carryover rate.     

Strategic entry deterrence and terrorism: Theory and experimental evidence

Using a two stage rent-seeking framework, we present a simple model of strategic entry/terrorism deterrence and test the model using laboratory experiments. Our contest success function highlights the potential for strategic spillovers. The theory illustrates that, relative to a cooperative outcome, negative externalities lead to over-spending on deterrence and positive externalities lead to under-spending on deterrence. Our experimental results are broadly consistent; subjects in the negative externality treatment had higher expenditures. In contrast to theoretical predictions, participation decisions, while primarily driven by the probability of winning a contest, were influenced by a subject’s ability to participate in multiple contests.     

Group specific public goods, orchestration of interest groups with free riding

We consider a situation in which two groups contest group-specific public goods. Each member of the group may have a different valuation of the prize. Our model can be interpreted as the contestants’ cost of lobbying efforts being non-linear, or the returns to their efforts being decreasing. We show that the level of free-riding depends on the return of the investment. We consider the situation under which one group initiates a contest to which different individuals and/or groups can be added. The question we pose is what is the optimal structure of additional groups?     

Symmetric two-stage contests with budget constraints

The impact of a budget constraint on individual expenditures is examined in two models of two-stage contests with homogenous and risk-neutral players competing to win a single, indivisible, commonly valued rent. The set of players is partitioned into equally sized groups. In the first model, one contestant from each group survives to compete on the second stage against the other survivors. In the second model, one group survives the first stage and its members compete against each other on the second stage. We derive and discuss the symmetric subgame perfect equilibrium solution for each 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.     

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.     

Bribing potential entrants in a rent-seeking contest

We consider a two-stage model of a Tullock rent-seeking contest where one new potential entrant makes his appearance. In the first stage each other player can contribute to bribe this new player to commit not to enter the contest. In the second stage we have the actual contest either with or without the new player. We present the conditions such that there exist equilibria in which the new player is being bribed.     

The strategic advantage of interdependent preferences in rent-seeking contests

We study rent-seeking contests, where the set of players contains two groups of players – one with independent preferences and the other with (negatively) interdependent preferences. It turns out that the latter experience a strategic advantage in general two-player contests and in n-player-contests with non-increasing marginal efficiency. For general n-player contests with increasing marginal efficiency, the strategic advantage prevails provIDed convexity of contest technologies is sufficiently weak. For strongly convex contest technologies, other types of equilibria exist, including one where indivIDualists receive strictly higher pay-off.     

On disclosure policy in contests with stochastic entry

We study how a contest organizer who seeks to maximize participant effort should disclose the information on the actual number of contestants in an imperfectly discriminatory contest with stochastic entry. When each potential contestant has a fixed probability of entering the contest, the optimal disclosure policy depends crucially on the properties of the characteristic function H(?)=f(?)/f ^??(?), where f(?) is the impact function. The contest organizer prefers full disclosure (full concealment) if H(?) is strictly concave (strictly convex). However, the expected equilibrium effort is independent of the prevailing information disclosure policy if a linear H(?) (Tullock Contest) applies.     

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.     

From weakest-link to best-shot: The voluntary provision of public goods

It has traditionally been assumed that the socially available amount X of a public good is the simple sum of the separate amounts x _i produced by the i = 1, ..., I members of the community. But there are many other possibilities of practical importance. Among them are: (i) Weakest-link rule, where the socially available amount is the minimum of the quantities individually provided, and (ii) Best-shot rule, where the socially available amount is the maximum of the individual quantities. The former tends to arise in linear situations, where each individual has a veto on the total to be provided (e.g., if each is responsible for one link of a chain); the latter tends to arise when there is a single prize of overwhelming importance for the community, with any individual's effort having a chance of securing the prize. In comparison with the standard Summation formula of ordinary public-good theory, it is shown that underprovision of the public good tends to considerably moderated when the Weakest-link function is applicable, but aggravated when the Best-shot function is applicable. In time of disaster, where the survival of the community may depend upon each person's doing his duty, the conditions for applicability of the Weakest-link rule are approximated. This circumstance explains the historical observation that disaster conditions tend to elicit an extraordinary amount of unselfish behavior.     

ABA ratings: what do they really measure?

Several recent spatial modeling studies incorporate valence issues—e.g., voters’ evaluations of the candidates’ competence, integrity, and charisma—that may give one of the candidates an electoral advantage that is independent of his policy positions. However to date all such models assume that while voters value positive valence characteristics, the candidates themselves do not. We develop a spatial model where the candidates are valence-seeking, i.e.—like the voters—the candidates prefer that the winning candidate possess qualities, such as integrity, diligence, and competence, that will enhance his job performance. We analyze a spatial model where the candidates value both the valence qualities and the policies of the winning candidate, and we show that the candidates’ optimal policy choices typically diverge as the valence differential between them increases, and in particular that the valence-disadvantaged candidate normally has incentives to become more extreme as the valence advantage of her opponent increases.     

Conflict and rent-seeking success functions: Ratio vs. difference models of relative success

The rent-seeking competitions studied by economists fall within a much broader category of conflict interactions that also includes military combats, election campaigns, industrial disputes, lawsuits, and sibling rivalries. In the rent-seeking literature, each party's success p_i (which can be interpreted either as the probability of victory or as the proportion of the prize won) has usually been taken to be a function of the ratio of the respective resource commitments. Alternatively, however, p_i may instead be a function of the difference between the parties' commitments to the contest. The Contest Success Function (CSF) for the difference from is a logistic curve in which, as is consistent with military experience, increasing returns apply up to an inflection point at equal resource commitments. A crucial flaw of the traditional ratio model is that neither onesided submission nor two-sided peace between the parties can ever occur as a Cournot equilibrium. In contrast, both of these outcomes are entirely consistent with a model in which success is a function of the difference between the parties' resource commitments.In preparing successive drafts of this paper I have benefited from suggestions and comments from Michele Boldrin, Avinash Dixit, Arye L. Hillman, David Hirshleifer, Eric S. Maskin, David Levine, Eric Rasmusen, John G. Riley, Russell Roberts, and Leo K. Simon.