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.     

Endogenous entry in contests

We report the results of laboratory experiments on rent-seeking contests with endogenous participation. Theory predicts that (a) contest entry and rent-seeking expenditures increase with the size of the prize and (b) earnings are equalized between the contest and the outside option. While the directional predictions offered in (a) are supported in the data, the level predictions are not. Prediction (b) is not supported in the data: when the prize is large, contest participants earn more than the outside option. When the prize is small, contest participants earn less. Previous studies of gender and contest competition suggest that females should (a) not perform as well in the contest; and (b) enter at a lower rate. We find some support for (a) but not for (b). Women participate in the contest at the same rate as men.     

Optimal contest design: volume and timing of rent seeking in contests

This paper undertakes a comparative analysis of rent-seeking contests in terms of the amount and the timing of effort they elicit from the participants. The optimal contest structure—the one that maximizes the discounted sum of efforts—is found to hinge on the degree of impatience of the contest organizers, the more patient of whom prefer longer contests consisting of pairwise matches among the contestants. Heterogeneity of the contestants' quality also turns out to play an important role in the comparison.     

Evolutionary equilibrium in Tullock contests: spite and overdissipation

Tullock's analysis of rent-seeking as a contest is reconsidered from an evolutionary point of view. We show that evolutionarily stable behavior in a Tullock contest exists and differs from behavior in Nash equilibrium. Evolutionarily stable behavior in these contests is robust in a strong sense and may entail overdissipation of the contested rent.     

PUBLIC GOODS,RENT DISSIPATION,AND CANDIDATE COMPETITION*

The early literature on rent seeking presumed that total expenditures in the rent-seeking process would equal the value of a contested prize. Subsequent analysis has shown, however, that a number of circumstances give rise to underdissipation of the contested rent—imperfectly discriminating contests, risk-aversion, or where individuals' valuations of the prize are not identical. This paper shows how underdissipation is associated with the public-good character of contested rents. In particular, total rent dissipation is demonstrated to be less than the average stake of the individual contenders. In addition to assessing rent dissipation in contests for public-good allocations, the paper also endogenizes the value of the prize by placing the rent-seeking contest in a setting of candidate competition.     

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.     

Endogenous contest success functions: a mechanism design approach

We describe optimal contest success functions (CSF) which maximize expected revenues of an administrator who allocates under informational asymmetry a source of rent among competing bidders. It is shown that in the case of independent private values rent administrator’s optimal mechanism can always be implemented via some CSFs as posited by Tullock. Optimal endogenous CSFs have properties which are often assumed a priori as plausible features of rent-seeking contests; the paper therefore validates such assumptions for a broad class of contests. Various extensions or optimal CSFs are analyzed.     

Population uncertainty in contests

Summary. We study contests where the set of players is a random variable. If it is known for certain that there will be at least one participant, then aggregate contest expenditure in equilibrium is strictly lower in a contest with population uncertainty than in a non-uncertain contest with the same expected number of players. This suggests an explanation of, for example, why empirical studies show rent-seeking expenditures to be much lower than predicted by other theories.Received: 29 June 2003, Revised: 14 December 2004, JEL Classification Numbers: C72, D44, D72, D82, K41. Correspondence to: Karl Wärneryd     

Equilibria in rent-seeking contests with homogeneous success functions

Summary. We characterize pure-strategy Nash equilibria for symmetric rent-seeking contests in which the contest success function is homogeneous of degree zero. The equilibrium strategies have a simple form. We give sufficient conditions for existence of an equilibrium.Received: 11 February 2003, Revised: 27 August 2004, JEL Classification Numbers: D72. Correspondence to: Andrew J. YatesWe thank Douglas Nelson, Jac Heckelman, and two anonymous referees for helpful comments.     

Overbidding and overspreading in rent-seeking experiments: Cost structure and prize allocation rules

We study experimentally the effects of cost structure and prize allocation rules on the performance of rent-seeking contests. Most previous studies use a lottery prize rule and linear cost, and find both overbidding relative to the Nash equilibrium prediction and significant variation of efforts, which we term ‘overspreading.’ We investigate the effects of allocating the prize by a lottery versus sharing it proportionally, and of convex versus linear costs of effort, while holding fixed the Nash equilibrium prediction for effort. We find the share rule results in average effort closer to the Nash prediction, and lower variation of effort. Combining the share rule with a convex cost function further enhances these results. We can explain a significant amount of non-equilibrium behavior by features of the experimental design. These results contribute towards design guidelines for contests based on behavioral principles that take into account implementation features of a contest.     

Repeated Contests with Asymmetric Information

The same contestants often meet repeatedly in contests. Behavior in a contest potentially provides information with regard to one's type and can therefore influence the behavior of the opponents in later contests. This paper shows that if effort is observable, this can induce a ratchet effect in contests: high ability contestants sometimes put in little effort in an early round in order to make the opponents believe that they are of little ability. The effect reduces overall effort and increases equilibrium utility of the contestants when compared with two unrelated one-shot contests. It does, however, also introduce an allocative inefficiency since sometimes a contestant with a low valuation wins. The model assumes an imperfectly discriminating contest. In an extension I show that, qualitatively, results are similar in a perfectly discriminating contest (all pay auction).     

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 optimal multi-stage contest

This paper investigates the optimal (effort-maximizing) structure of multi-stage sequential-elimination contests. We allow the contest organizer to design the contest structure using two instruments: contest sequence (the number of stages, and the number of contestants remaining after each stage), and prize allocation. When the contest technology is sufficiently noisy, we find that multi-stage contests elicit more effort than single-stage contests. For concave and moderately convex impact functions, the contest organizer should allocate the entire prize purse to a single final prize, regardless of the contest sequence. Additional stages always increase total effort. Therefore, the optimal contest eliminates one contestant at each stage until the finale when a single winner obtains the entire prize purse. Our results thus rationalize various forms of multi-stage contests that are conducted in the real world.     

RENT-SEEKING FIRMS AND CONSUMERS: AN EQUILIBRIUM ANALYSIS*

This paper examines the probability of success in a rent-seeking contest as a general function of the resources that both firms and consumers devote to lobbying the government. The object of lobbying is a possible restriction of market supply, where the likelihood that supply will be restricted to a given extent depends on everyone's lobbying efforts. In equilibrium the expected social loss due to rent-seeking activities is at most equal to the size of the contested rent, and this upper bound does not depend on the active participation of consumers in the contest. Markets in which supply is not restricted may also be associated with rent-seeking waste. Finally, consumers' rent-seeking efforts are shown to be socially productive, both on the margin and in total.     

The King Never Emigrates

This paper uses a locational model of rent-seeking to describe incentives to emigrate. A country is considered in which how a person fares in privileged income redistribution is determined by proximity to a king. Contests for privilege determine whether the more or the less productive in the population are located closer to the king. A distinction is drawn between contests for privilege that are "easy" and "difficult." When contests are "easy," the more productive are furthest from the king and emigrate first. When contests are "difficult," the least productive emigrate first. In either case, the population begins to unravel.     

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.     

在线创新竞赛的基本问题与研究展望

在线创新竞赛是组织实施开放式创新的新途径,学术界关于在线创新竞赛的研究日益丰富。然而,现有文献分布于心理学、经济学、管理学、教育学等各个领域,为了梳理现有研究成果并展望未来研究方向,分别从什么是在线创新竞赛、谁在参与在线创新竞赛和如何实施在线创新竞赛3个角度对现有文献进行了述评,厘清了在线创新竞赛的主要特征与类型、参与主体动机及要素设计等基本问题。最后,探讨了开放式创新和“互联网+”背景下,在线创新竞赛的未来研究方向。     

Orchestrating Rent Seeking Contests

Contests have different, sometimes quite complex, organisational structures. In particular, while most of the existing literature focusses on simultaneous contests, multistage contests are also quite frequently encountered. This paper seeks to provide a rationale for the latter by endogenising the choice of a contest structure, which is made by an organiser of a contest interested in maximising the efforts expended by the contenders.     

Dynamic Multi‐Activity Contests*

We develop a model of dynamic multi‐activity contests. Players simultaneously choose efforts in long‐run activities, observe each other's efforts in these activities, and then simultaneously choose efforts in short‐run activities. A player's long‐run and short‐run efforts complement each other in determining the player's probability of winning. We compare the outcomes of this two‐stage model to those of the corresponding model in which players choose efforts in all activities simultaneously. Interestingly, effort expenditures are always lower in the sequential multi‐activity contest than in the simultaneous multi‐activity contest. The implications of this result for the organization of military, litigation, innovation, academic, and sporting contests are highlighted.     

Experimental comparison of multi-stage and one-stage contests

This article experimentally studies a two-stage elimination contest and compares its performance with a one-stage contest. Contrary to the theory, the two-stage contest generates higher revenue than the equivalent one-stage contest. There is significant over-dissipation in both stages of the two-stage contest and experience diminishes over-dissipation in the first stage but not in the second stage. Our experiment provides evidence that winning is a component in a subject's utility. A simple behavioral model that accounts for a non-monetary utility of winning can explain significant over-dissipation in both contests. It can also explain why the two-stage contest generates higher revenue than the equivalent one-stage contest.