Sequential Contests

We compare expected rent-seeking expenditures and efficiencyof simultaneous versus sequential rent-seeking contests. We find that when two risk neutral ex ante identical agents are competing,sequential contests are ex ante Pareto superior tosimultaneous contests. We then endogenize the timing decisionof rent-seeking expenditures and show that with ex anteidentical contestants, all subgame perfect equilibria of thisgame are sequential contests.     

Contests—a comparison of timing and information structures

We study a model of imperfectly discriminating contests with two ex ante symmetric agents. We consider four institutional settings: Contestants move either sequentially or simultaneously and in addition their types are either public or private information. We find that an effort-maximizing designer of the contest prefers the sequential to the simultaneous setting from an ex ante perspective. Moreover, the sequential contest Pareto dominates the simultaneous one when the contestants?? types are sufficiently negatively correlated. Regarding the information structure, the designer ex ante prefers private information while the contestants prefer public information.     

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.     

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.     

Legal expenditure as a rent-seeking game

Legal expenditures at a civil trial constitute an interesting type of rent-seeking contest. In civil litigation there is a natural interaction between the objective merits of the case and the outcome of the contest. Institutions such as fee shifting do not generally have a counterpart in other rent-seeking contests. The endogenous decision to participate in the rent-seeking contest corresponds to the decision by the plaintiff to bring a case, and the decision by the defendant to defend it. The desirability of fee shifting is very sensitive to the value of the parameter which describes the legal technology.     

Sequential contests revisited

In a past issue of this journal, Morgan (Public Choice 116:1–18, 2003) finds that aggregate effort is greater in sequential than in simultaneous lottery contests. We show that Morgan’s result is incorrect owing to a slip in a proof, and that aggregate effort turns out to be greater in sequential contests only if the contestants are sufficiently homogeneous. Additionally, we discuss the robustness of the corrected result to different specifications of the contest success function, and we partially restore Morgan’s case for sequential contests by showing that these contests are more desirable when maximizing only the effort of the winner, rather than maximizing the aggregate 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.     

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.     

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.     

Rent dissipation and efficiency in a contest with asymmetric valuations

This paper introduces contest efficiency as an alternative to rent dissipation when measuring efficiency in a contest with asymmetric valuations. Contest efficiency is defined as the expected proportion of the maximum obtainable benefit captured by the contest, and differs from rent dissipation because it values the expected winner of the contest. Therefore, rent dissipation and contest efficiency may suggest contradictory conclusions when agents have asymmetric valuations. This result is illustrated when comparing alternative equilibria in contests with asymmetric reimbursement and when analyzing the comparative static effect of a change in the relative benefit of two agents in a Cournot-Nash contest.     

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.     

The number of rent-seekers and aggregate rent-seeking expenditures: An unpleasant result

I examine a rent-seeking contest in which the winner gets a minimum rent but also gets an additional rent which is an increasing function of his lobbying expenditure. I give real-world examples of such rent-seeking competitions. Contrary to the standard result in the rent-seeking literature, I obtain the perverse result that aggregate rent-seeking expenditures may be inversely related to the number of rent-seekers. However, I note that even if this result holds, the cost of administering rent-seeking competitions may imply that society is better off with fewer contenders than with an infinitely large number of contenders, although the optimal number may not be the smallest number.     

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.     

Goods or resource contests?

In this paper we analyze the optimal mix between appropriative and defensive activities for goods (goods contest) and appropriative and defensive activities for resources (resource contest). We show that goods contests are qualitatively different from resource contests. It turns out that for plausible cases the resource contest is dominated by the goods contest in the sense that investments are only positive in the latter.     

Stakes and Welfare in Rent-Seeking Contests

Using a public-policy application ofTullock's two-player rent-seeking contest,this paper focuses on the relationshipbetween the aggregate expected utility ofthe players and their asymmetricvaluations. In our game these valuationsare the players' payoffs in the twopossible states of nature, namely, theapproval and rejection of the proposedpublic policy. Our main result provides thecondition that ensures that the aggregateexpected payoff of the two contestants (theinterest groups that compete on theapproval of the proposed policy) is positively related to the valuationparameters.     

Risk-aversion and prudence in rent-seeking games

This paper considers a common n-agent symmetric rent-seeking game. It derives conditions so that risk-aversion and risk always decrease rent-seeking efforts. These conditions hold for any regular contest success function when risk-averse rent-seekers are also prudent. Under n=2, prudence is a necessary and sufficient condition for risk-aversion to decrease rent-seeking efforts compared to risk-neutrality. An intuition for this result is given based on a self-protection model.     

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.     

Rent-seeking contests with incomplete information

We consider rent-seeking contests with two players who each have private information about their own cost of effort. We consider both discrete and continuous distributions of costs and give results for each case, focusing on existence of equilibrium.     

Winner-pay contests

We analyze winner-pay contests in which players select bids, the winner is determined probabilistically through a contest success function, and only the winner must pay her bid. We show that a pure-strategy Nash equilibrium exists and is unique under weak assumptions on the contest success function. We determine the Nash equilibrium for several examples. We also consider how equilibrium bids are influenced by private information about the value of winning the contest.