The solution to the Tullock rent-seeking game when R>2: Mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents.     

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.     

Ambiguous political power and contest efforts

When there is incomplete information on the source of power in a contest, the contestants may divide their lobbying efforts between the potential centers of power, only one of which determines the contests’ winning probabilities. Our analysis focuses on the effect of ambiguity regarding the source of power on the contestants’ aggregate effort in a symmetric, simple lottery contest with two potential centers of power. Specifically, we examine the effects of varying the informativeness of the contestants’ private signals (i.e., the probability that a signal is correct) and the degree of correlation between them. Our benchmark case is the standard Tullock’s model, in which the source of power is known, i.e., the contestants’ signals are perfectly informative. We show that the level of aggregate effort in this case is reached also when the signals are perfectly uninformative. However, in any intermediate case the contestants’ aggregate effort is lower, provided that the signals are not perfectly correlated. In other words, there is a U-shape relationship between the informativeness of the signals and the aggregate effort in the contest. The lowest level of effort is spent when the signals are independent and the probability that a signal is true is about 0.85. In this case, efforts are reduced by about one-fifth in comparison with the benchmark case: from a rent dissipation of 50% to slightly over 40%.     

Rent-seeking contests with private values and resale

This paper studies rent-seeking contests with private values and resale possibilities. With a stochastic success function, the resulting possible inefficiency creates a motive for aftermarket trade. Players’ valuations are determined endogenously when there is an opportunity of resale. We characterize symmetric equilibria. We assume that the winner has full bargaining power, but the results extend to other resale mechanisms. We show that resale enhances allocative efficiency ex post at the expense of more social resource waste since players compete more aggressively with resale possibilities.     

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.     

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.     

Crowding-out in productive and redistributive rent-seeking

This paper presents a general rent-seeking model in which participants decide on entry before choosing their levels of efforts. The conventional wisdom in the rent-seeking literature suggests that the rent dissipation increases with the number of potential participants and with their productivity of effort. In this paper, we show that this result of the rent-seeking literature is far from general and applies only when participants are relatively weak and enter the game with certainty. In the presence of strong competitors, the expected total dissipation actually decreases, since participation in the game is less frequent. We further consider the impact of competitors’ exit option, distinguishing between “redistributive rent-seeking” and “productive rent-seeking” situations. In redistributive rent-seeking, no social loss results from the fact that all competitors exit the race. In productive rent-seeking, instead, lack of participation creates a social loss (the “lost treasure” effect), since valuable rents are left unexploited. We show that the lost-treasure effect perfectly counterbalances the reduction in rent dissipation due to competitors’ exit. Hence, unlike redistributive rent-seeking, in productive rent-seeking the total social loss remains equal to the entire rent even when parties grow stronger or the number of players increases.     

Outsourcing in contests

We study ex post outsourcing of production in an imperfectly discriminating contest, interpreted here as a research tournament or a procurement contest for being awarded some production contract. We find that the possibility of outsourcing increases competition between the contestants, leading to higher total contest effort, if the contest winner is expected to obtain a sufficiently large share of ex post outsourcing rents. Under reasonable assumptions, outsourcing tends also to increase the number of active contestants, strengthening the case for outsourcing to increase total contest effort. If such effort is socially wasteful, outsourcing creates a welfare trade-off between ex ante and ex post efficiency.     

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.     

Transaction costs can encourage Coasean bargaining

When there are three parties, instability problems brought about by the emptiness of the core of the corresponding cooperative game may cause the Coase Theorem to fail, even when other more direct impediments to bargaining are low. We show that the standard Coasean bargaining game involving three parties is strategically equivalent to an asymmetric three-player majority game. Hence, when there are three parties, instability problems will cause the Coase Theorem to fail if and only if the core of the corresponding three-player majority game is empty. We use this equivalence result to derive all instances in which the Coase Theorem will and will not hold with three parties, and show that a priori, such instability problems are likely to be rare—the Coase Theorem will actually hold most (over 80 %) of the time. We also demonstrate that it is always possible to find a set of transaction costs which, when introduced into a frictionless bargaining situation, will cause an empty core to become non-empty. In other words, transaction costs can mitigate instability problems: situations exist in which the presence of transaction costs will cause the Coase Theorem to hold when, in the absence of those direct transaction costs, it would fail to hold. When there are three parties, rather than hindering agreements, the existence of direct transaction costs can sometimes—but not always—reduce instability and encourage Coasean bargaining.     

Can a contractarian be a paternalist? The logic of James M. Buchanan’s system

We consider the simplest version of a jungle economy à la Piccione-Rubinstein, wherein as many agents as goods are assumed, agents consume at most one indivisible good, and a transitive strong power relation exists. We first study the wilderness of jungle equilibria, i.e., whether they are Pareto-minimal (an allocation is Pareto-minimal if it is impossible to reduce the welfare of one agent without increasing the welfare of another). We show that jungle equilibria are not necessarily Pareto-minimal. We then study and characterize the set of Pareto-minimal jungle equilibria. Second, we tackle the case of equally powerful people, in contrast to the assumption that the power relation is asymetric. Assuming specifically a transitive weak power relation, we show that jungle equilibria exist, but that they are not always unique, nor Pareto-optimal. We also provide conditions under which those equilibria are Pareto-minimal.

     

A generalized model of rent-seeking behavior

In this paper I present a formal analysis of rent-seeking games in which the players' valuations for the prize are represented as vectors. The players in this game are risk neutral and may not be indifferent to who wins the contestable rent if it is someone else. Both Tullock's original rent-seeking model and the public goods rent-seeking model by Katz et al. turn out to be special cases of this more general model.     

The Political Economy of Gender: Explaining Cross-National Variation in the Gender Division of Labor and the Gender Voting Gap

Mainstream political economy has tended to treat the family as a unit when examining the distributional consequences of labor market institutions and of public policy. In a world with high divorce rates, we argue that this simplification is more likely to obscure than to instruct. We find that labor market opportunities for women, which vary systematically with the position of countries in the international division of labor and with the structure of the welfare state, affect women's bargaining power within the family and as a result, can explain much of the cross country variation in the gender division of labor as well as the gender gap in political preferences.     

Rent dissipation when rent seekers are budget constrained

In the original Tullock (1975, 1980) game, an individual bidder's probability of winning with a bid b is proportional to b^R, where the exponent reflects economies of scale in rent seeking. Different interpretations can be given to these probabilities. First, one may view R as a reflection of the political culture. Alternatively, one may view R as a choice variable for a politician. Intuition suggests that a society with a high tolerance for the selling of political favors and politicians who are receptive to rent seeking would both induce greater rent-seeking expenditures than other societies, all else equal. This paper shows that a lower value of R can actually lead to more rent dissipation than a higher value. This paper also reinforces two points concerning rent seeking. First, the analysis confirms the robustness of under-dissipation of rents, even in the face of entry. Second, it points out the importance of distinguishing between rent-seeking expenditures and rent dissipation. When bidders must borrow, for example, total expenditure may understate rent dissipation.     

Constitutional Prohibitions in a Rent Seeking Model

I extend the standard rent seeking model to allow lobbying fora constitutional prohibition on wealth transfers. I examinetwo issues: (1) the ability of special interests withsignificant political capacity to block constitutional change;and (2) the effect of adding a constitutional stage on totallobbying expenditures. Defeating a prohibition on wealthtransfers is a public good for rent seekers; success inconstitutional politics merely allows them to lobby for wealthtransfers. The resulting collective action problem for rentseekers in constitutional politics offsets the generalinterest's free rider problems, reducing the probability oftransfers and expected total lobbying expenditures compared tothe traditional rent seeking contest. Introduction of aconstitutional stage also reverses several comparative staticsresults from the rent seeking game. An increase in the numberof rent seekers or the general interest's (consumers') abilityto organize increase lobbying in the rent seeking game butgenerally reduce expected lobbying in the constitutionalprohibition game.     

Contests with an unknown number of contestants

This paper studies rent-seeking contests where the contestants do not know the number of actively competing contestants. Two models are compared. In the first, all players are risk neutral; in the second, all have constant absolute risk aversion. If the expected fraction of active contestants is low, an increase in the number of potential contestants increases individual rent-seeking efforts. This effect is in contrast to the complete information case where individual rent-seeking efforts decrease in the number of contestants. The effect is more likely under risk neutrality, but also possible under risk aversion. Equilibrium rent seeking efforts are lower under risk aversion if and only if the expected fraction of active contestants is low.     

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.     

Parliamentary procedure: principal forms and political effects

A standard conclusion of theorists who model bargaining as a non-cooperative game is that the party designated to make the first move—the formateur party—will determine the bargaining outcome. Most empirical studies of parliamentary coalition formation have paid surprisingly little attention to the formation process. In this paper we model government formation as a two-stage unordered discrete choice problem that better reflects this process. The first step involves the selection of a formateur party, and the second involves the choice of partners by the predicted formateur. We evaluate several hypotheses for the two stages, using a data set of all cabinets formed in the Western European countries from 1970 to 2006. In our analyses of formateur selection, we find that party size is clearly the dominant feature. In the second stage, we show that when predicting government composition it is fruitful to add information drawn from a first stage analysis.     

Asymmetric contests with liquidity constraints

We consider two bidders with asymmetric valuations competing to win an exogenous prize. Capital markets are imperfect, such that the contestants possibly face a liquidity constraint. We show that aggregate investments are lower if at least one bidder has a liquidity constraint, even if the low-valuation bidder possibly increases his/her investments. Furthermore, the effect of the high-valuation bidder’s liquidity constraint on competitive balance is ambiguous. However, if the low-valuation bidder is constrained, greater wealth unambiguously increases competitive balance. Surprisingly, if the low-valuation bidder has a constraint, a tighter constraint can increase his/her profit.     

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.