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.     

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.     

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.     

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.     

On Norms and Coordination Games: A Rent–Seeking Approach

The aim of this paper is to extend the rent–seeking literature to the equilibrium selection problem in competitive coordination games, i.e., games in which more than one equilibrium exists, and individuals' preferences are opposed. We analyze alternative correlated equilibria: contractual agreements and legally enforced equilibria. The latter are to be understood as the outcome of rents–seeking contests in which players invest resources in order to set a norm. The contest is analyzed in its basic two–person setting and later generalized to the two–populations case. There we show that the outcomes depend on the relative payoff structure of the game, the technological properties of the contest, and the population distribution. Finally, the efficiency analysis focuses not only on the extent of the rent dissipation, but also on the comparative analysis of the inefficiencies that arise in the market (not coordinated) equilibrium.     

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.     

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.     

INTENSITY OF COMPETITION, ENTRY AND ENTRY DETERRENCE IN RENT SEEKING CONTESTS

In rent seeking contests agents compete over a given amount of resource a prize. To increase the likelihood of winning the prize, the agents expend efforts. This paper addresses the issue of entry to and entry deterrence from rent seeking contest. The main purpose of the analysis is to provide an explanation for the empirical fact that the number of participants in contests is usually small. I also obtain results on the relationship between the intensity of competition in a contest and the amount of the contenders'expenditures.     

Complements and substitutes in common agency

In this paper we analyse the problem of the rent obtained by the agent in private common agency games. The key features for answering this question are the properties of the cost function of the agent. We prove that if this cost function is submodular (costs complements) then there is no equilibrium in which the agent makes a rent and if the cost function is supermodular (costs substitutes) then in all equilibria the agent makes a rent. We also examine the problem in some intermediate cases.     

Multi-stage sequential all-pay auctions

We study multi-stage sequential all-pay contests (auctions) where heterogeneous contestants are privately informed about a parameter (ability) that affects their cost of effort. We characterize the perfect Bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants׳ expected highest effort.     

Asymmetric contests with general technologies

Summary. We investigate the pure-strategy Nash equilibria of asymmetric, winner-take-all, imperfectly discriminating contests, focussing on existence, uniqueness and rent dissipation. When the contest success function is determined by a production function with decreasing returns for each contestant, there is a unique pure-strategy equilibrium. If marginal product is also bounded, limiting total expenditure is equal to the value of the prize in large contests even if contestants differ. Partial dissipation occurs only when infinite marginal products are permitted. Our analysis relies heavily on the use of share functions and we discuss their theory and application.Received: 28 May 2003, Revised: 26 April 2004, JEL Classification Numbers: C72, D72. Correspondence to: Richard CornesMuch of the research in this paper was undertaken while the first author was a Visiting Scholar at the Centre for Economic Studies, University of Munich. The support of the Centre is gratefully acknowledged.     

Governing Interest Groups and Rent Dissipation

In a contest of group‐specific public goods we consider the effect that managing an interest group has on the rent dissipation and the total expected payoffs of the contest. While in the first group there is a central planner determining its members’ expenditure in the contest, in the second group there are two different possibilities: either all the members are governed by a central planner or they are not. We consider both types of contests: an all‐pay auction and a Logit contest success function. We show that while governing an interest group decreases free‐riding, it may as well decrease the rent dissipation; at the same time the expected payoffs of the groups may also decrease.     

Contests with rank-order spillovers

This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player??s strategy generates direct or indirect affine ??spillover?? effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests.     

An experimental study of bidding in contests of incomplete information

In many contest situations, such as R&D competition and rent seeking, participants’ costs are private information. We report the results of an experimental study of bidding in contests under different information and symmetry conditions about players’ costs of effort. The theory predicts qualitatively different comparative statics between bids under complete and incomplete information in contests of two and more than two players. We use a 2×3 experimental design, (n=2, n=4)×(symmetric complete information, asymmetric complete information, incomplete information), to test the theoretical predictions. We find the comparative statics of bids across the information and symmetry conditions, and the qualitative differences in comparative statics across group sizes, in partial agreement with the theory.     

Tournaments of Weakly Heterogeneous Players

We consider three prominent tournament formats—contests, binary elimination tournaments, and round-robin tournaments—in the case when players are heterogeneous in their abilities but the heterogeneity is, in a well-defined sense, weak. Using linear approximation, we characterize equilibrium strategies and payoffs in the three tournament games and compare them to the benchmark symmetric case of identical players. We describe small deviations from the symmetric equilibria by elasticities of a player's equilibrium effort with respect to her own ability and the abilities of her rivals. Our results only require general symmetry and smoothness assumptions but not specific functional forms for the probabilities of winning in tournaments. We show that, in equilibrium: (i) a player's effort and payoff depend on her rivals' abilities in a model-independent way, either through the average ability of the field (for static games), or through the properly discounted average ability of the field (for dynamic elimination tournaments); (ii) players respond stronger to changes in their own relative abilities than to changes in their rivals' relative abilities; (iii) aggregate effort (dissipated rent) does not change compared to the benchmark case; (iv) it is not possible to manipulate aggregate effort through seeding in binary elimination tournaments, although optimal seeding schemes for other purposes can be identified; and (v) balanced seeding and a uniform distribution of relative abilities cancel out the dependence of a player's effort on her rivals' abilities in binary elimination tournaments.     

DISCRIMINATION IN A MODEL OF CONTESTS WITH INCOMPLETE INFORMATION ABOUT ABILITY

We study contests with private information and identical contestants, where contestants' efforts and innate abilities generate output of varying qualities. The designer's revenue depends on the quality of the output, and she offers a reward to the contestant achieving the highest quality. We characterize the equilibrium behavior, outcomes, and payoffs for both nondiscriminatory and discriminatory (where the reward is contestant‐dependent) contests. We derive conditions under which the designer obtains a larger payoff when using a discriminatory contest and describe settings, where these conditions are satisfied.     

The Economics of Tenancy Rent Control

We consider a rent control regime where rent increases on, and eviction of, a sitting tenant are forbidden. When apartments become vacant landlords may negotiate new rents. If inflation exists, landlords prefer to rent to short-staying tenants. Since departure-date-contingent contracts are forbidden and landlords cannot tell whether tenants are short-stayers, an adverse selection problem arises, with a Pareto inefficient equilibrium. When tenant types are determined endogenously, multiple equilibria can arise where one equilibrium is Pareto dominated. Abolition of the rent control regime, cannot only shift the equilibrium out of this inferior outcome, but also result in across-the-board lowering of rents.     

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.     

Complementarity in contests

To facilitate the study of contests in general equilibrium, we examine winner-take-all contests in which the prize is complementary to the effort of the contestants, as inputs are in production functions or final goods in utility functions. We focus on the effects of technological factors and endowments on the effort and the welfare of the contestants. Most of our findings differ considerably from the standard model of contests in which prize and effort are independent. In particular, we find a critical role for the elasticity of substitution between prize and effort. For example, under low elasticities of substitution, a higher prize reduces the effort exerted by the contestants.     

Unfair contests

Real-world contests are often “unfair” in the sense that outperforming all rivals may not be enough to be the winner, because some contestants are favored by the allocation rule, while others are handicapped. This paper analyzes an unfair, two-player discriminatory contest (all-pay auction) with private values. We characterize equilibrium strategies, provide closed form solutions, and illustrate additional strategic issues arising in such unfair contests.