Tullock contests of weakly heterogeneous players

I explore asymmetric equilibria in a Tullock contest of heterogeneous players in the case when the players’ heterogeneity is weak, and the effort optimization problem can be analyzed in the linear approximation. With increasing discriminatory power of the contest, players sequentially drop out. The corresponding threshold values of the discriminatory power are related to those identified earlier for a Tullock contest of identical players. Weak heterogeneity, however, is sufficient to make the players’ behavior strongly asymmetric and qualitatively alter the structure of the equilibria as compared to the homogeneous case.     

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.     

Learning the structure of a simple rent-seeking game

This paper considers a form of the Tullock imperfectly discriminating rent-seeking game in which the contestants are uncertain about the value of a bias parameter in the probability of winning function. Beliefs about this unknown parameter are not constrained to be static; we consider two methods by which the players' prior beliefs on this parameter can be updated. First, we allow for information to emerge by considering the case in which the game is played twice, with the outcome of the first game known before the second begins. The identity of the winner of the first contest represents information which emerges endogenously that can be used to revise beliefs on the unknown bias parameter. Second, information can be produced outside of the model by an external agency; this gives rise to exogenous learning. We consider the consequences for rent-seeking in each of these two cases.     

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%.     

Tullock’s contest with reimbursements

We consider Tullock’s contest with reimbursements. It turns out that the winner-reimbursed contest maximizes net total spending while the loser-reimbursed contest minimizes net total spending. We investigate properties of contests with reimbursements and compare them with Tullock’s classic contest. Applications for R&D, government contracts, and elections are discussed.     

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.     

Imperfect rent dissipation with unionized labor

Traditional rent-seeking theory focused only on socially wasteful expenditures by firms competing for restrictive regulations. More recently, rent-defending expenditures by consumers have also been taken into account. This paper extends the analysis by adding rent-sharing expenditures by organized labor. The paper merges the Tullock lottery model and the monopoly union model and considers both a costless and a costly wage bargaining mechanism. The participation of consumers and workers in the distributional contest is shown to reduce, rather than increase, the social cost of restrictive regulations. The participation of consumers and workers also raises the probability of deregulation.     

A generalized Tullock contest

We construct a generalized Tullock contest under complete information where contingent upon winning or losing, the payoff of a player is a linear function of prizes, own effort, and the effort of the rival. This structure nests a number of existing contests in the literature and can be used to analyze new types of contests. We characterize the unique symmetric equilibrium and show that small parameter modifications may lead to substantially different types of contests and hence different equilibrium effort levels.     

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.     

The Politics of Bureaucracy and the failure of post-war reconstruction

Gordon Tullock’s The Politics of Bureaucracy must be considered one of the most important works on bureaucracy ever written. In this paper, I argue that Tullock’s analysis of bureaucracy is as relevant as ever. To support this claim, I focus on U.S.-led reconstruction efforts which attempt to export liberal democracy via military occupation. Bureaucratic organizations play a key role in these reconstruction efforts and as such, Tullock’s analysis is directly relevant. It is argued that Tullock’s study clarifies not just the limits of bureaucratic activity, but also the importance of spontaneous orders for coordinating activities outside those limits and generating the very institutional context in which liberal democracy can evolve and sustain. The main conclusion is that the nature of public bureaucracy constrains the ability of the United States to exogenously impose liberal democratic institutions in foreign countries for the very reasons Tullock emphasized long ago.     

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.     

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.     

Child-raising cost and fertility from a contest perspective

Public Choice - We model parents’ fertility and child-raising spending decisions as a Tullock contest with budget constraints and prizes that depend on relative efforts. We show that if the...     

Rents, dissipation and lost treasures: Comment

In an interesting recent paper, Dari-Mattiacci and Parisi (2005) extended Tullock's (1980) rent-seeking game with an entry decision. The mixed strategies identified by Dari-Mattiacci and Parisi for the case of increasing returns in the contest success function (r2) do not constitute an equilibrium of the game they study. However, these strategies are an equilibrium if the strategy space of the game is restricted by a minimum expenditure requirement, and this minimum expenditure requirement is an element of a specific interval.     

A stochastic derivation of the ratio form of contest success functions

This note provides a distribution-based justification for the ratio form of contest success functions (CSFs), in which a player’s success depends positively on her effort relative to that of her opponents. I show that the inverse exponential distribution of the random shocks yields the ratio form. Extending this approach to asymmetric contests, I also derive an asymmetric ratio form of CSFs.     

Maximizing behavior & market forces: the microfoundations of spontaneous order theorizing in Gordon Tullock’s contributions to Smithian political economy

I explore the microfoundations of Gordon Tullock’s contributions to political economy and argue that his approach is consistent with the “invisible hand” theorizing of Adam Smith. While Smith (and Hayek) are celebrated for their emphasis on the “bright-side” of spontaneous social cooperation, Tullock emphasized the “dark-side” of social processes when the incentives are perverse and information is distorted. By explicating the microfoundations of Tullock’s rendering of Smithian political economy this paper will set the stage for a reassessment of Tullock as a spontaneous order theorist.     

Autocracy and coups d’etat

In this paper I first briefly survey Tullock’s contributions to the study of autocracy and coups d’etat. Tullock’s analysis of the coup d’etat is insightful. He suggested that those at the top could control those at the bottom with a proper system of incentive payments. Here I expand on that idea by asking the reverse question, not what keeps those at the bottom from rebelling, but what keeps those at the top from looting the regime? I begin by noting that shareholders of the modern widely held corporation face a similar problem: what keeps the CEO from looting the company when the market for corporate control is flawed, shareholders are too weak to exercise discipline, and the board is in the CEO’s pocket? I suggest the answer is provided by “internal governance”: the old need the young for good performance. I explain the financial crisis of 2008 as in part the result of the failure of this mechanism. I also explain the success of modern China this way: The Communist Party facilitates growth because its structure provides a way for superiors (the “old”) to trade with subordinates (the “young”). I have also expanded on Tullock’s analysis to ask what conditions might prevent the dictator from implementing his solution to the coup d’etat problem, thus explaining why coups d’etats actually occur. The basic reason is the weakness of the state. Japanese history provides two interesting illustrations of this: first the Tokugawa regime, where the people were over-controlled, and second, the Meiji constitution, implemented after the fall of the Tokugawa state. The Japanese problem after Meiji was that the military (the young) had no incentive to offer their loyalty to the old (the civilian regime), so the young acted on their own. The problem was the reverse of the Tokugawa regime’s: the Meiji constitution left the bottom with too much control over the top. There was no formal coup d’etat but a number of coup attempts were made and de facto the military increasingly constituted a state within a state. This reversal of authority apparently continued down the chain of command, ultimately with tragic consequences, most notably the invasion of Pearl Harbor.     

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.     

Coordination without command: Stretching the scope of spontaneous order

How far can we stretch the scope of spontaneous order? Gordon Tullock’s important work on the economics of non-human societies shows how these societies are able to coordinate without command despite features economists typically see as limiting the scope of spontaneous order. Using Tullock’s insights, I search for the “human ant nest”—spontaneous institutional arrangements that create human cooperation despite the presence of these obstacles. I find two significant examples of this, both in precolonial Africa. The first demonstrates the effectiveness of spontaneous order in the face of threats of violent theft. The second shows the effectiveness of spontaneous order in the face of social heterogeneity. These cases suggest a broader scope for spontaneous order than conventional wisdom permits.     

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.