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.     

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.     

Activity and inactivity in a rent-seeking contest with private information

We consider a rent-seeking contest in which one player has private information about his own valuation of the prize. This valuation may be either high or low. All other players have a known and identical valuation of the prize. We present necessary and sufficient conditions under which the privately informed player exerts a positive or zero equilibrium effort.     

A multi-winner nested rent-seeking contest

Public Choice - This paper considers a symmetric imperfectly discriminating rent-seeking contest in which there may be several winners. We first demonstrate a serious flaw in previous work and then...     

Price discrimination in a rent-seeking economy

This paper examines the incentive and the consequences of using discriminatory pricing by a monopolist in a rent-seeking economy. It is shown that, even if all consumer groups' demands have identical elasticities at any given price, the monopolist has an incentive to charge a lower price to high pressure consumer groups so as to alleviate their rent-seeking efforts in challenging its monopolistic power. Furthermore, it is shown that by allowing the firm to price discriminate total welfare may increase, even if all rent-seeking expenditures are completely wasteful.     

Corporate political offices in a rent-seeking society

This paper examines agent discretion that is a result of the structure of the legislative process. Based on several distributions of lawmaking powers, different games are analyzed in which players decide on regulatory policies. The analysis shows that agent discretion increases as lawmaking powers are differentiated and assigned to specialized players. Particularly, monopoly initiation power, which allows a player to act as a gatekeeper, has a substantial impact on discretion. Agent discretion will be even larger when these players also have heterogenous preferences. The framework that is developed in this paper permits comparisons across different political systems with regard to agent discretion and legislative control on policymaking.     

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.     

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.     

Risk aversion in two-period rent-seeking games

This work analyzes a two-period rent-seeking game, with the aim of studying the effect of risk aversion on the optimal choices made by the rent-seekers. We first prove that the equilibrium in two-period rent-seeking games always is unique. The analysis also shows that more risk aversion reduces the investment in the rent-seeking game in a two-period framework without introducing the additional condition of prudence, required in one-period models. Similarly, the introduction of a risky rent, instead of a given rent, implies, in the two-period framework, a reduction in investment under the condition that the rent-seekers are risk averse. Moreover, with risk aversion, larger first-period wealth increases investment in the rent-seeking game and larger second-period wealth reduces it. When both first-period and second-period wealth increase, investment in the rent-seeking game declines if the rent-seeker is risk averse and imprudent. Lastly, when a risky level of second-period wealth is introduced, the rent-seeker increases (reduces) investment in the rent-seeking game if he is risk averse and prudent (imprudent).

     

Endogenous sharing rules in collective-group rent-seeking

This paper examines the possibility of endogenous determination of intra-group sharing rules in a collective-group rent-seeking game. Collective-group rent-seeking is considered as a two-stage Nash-Cournot game in which sharing rules are determined prior to individual decision on voluntary contribution. The solution is subgame perfect and is obtained by backward induction. In competition between two groups of the same size, the Nash equilibrium sharing rule of each group is to distribute rent to each according to relative effort. Total rent-seeking outlays in this case are equal to those obtained by Tullock (1980). When more than two groups compete for a rent, the sharing rule based on relative effort is again likely to be the Nash equilibrium strategy of each group. The amount of total rent-seeking outlays is also equal to that in Tullock (1980). In a nutshell, the rent is substantially dissipated if sharing rules are endogenously determined.     

A contest success function with a tractable noise parameter

I propose a simple contest success function which is a variant of the Tullock probability function under certain conditions. It relaxes two features of the Tullock probability function. I show that this contest success function could be used to obtain interesting results and is more tractable than Tullock's function in certain cases. In particular, researchers who are interested in examining the degree to which luck as opposed to effort affects behavior in different contest settings might find it easier to use this contest success function than the Tullock success function. Unlike the Tullock function, there always exists a pure-strategy equilibrium for all values of the parameter which captures the degree of noise. The proposed function has been used in Kolmar and Wagener (2004) with interesting results.     

An analysis of rent-seeking games with relative-payoff maximizers

In this paper, we introduce relative-payoff maximizing firms into the Tullock model of rent-seeking. These firms try to realize higher (expected) payoff than other firms. As a consequence of this, the outcome of the model changes: Firms, on average, will invest more in the rent-seeking process, the rate of dissipation of the rent becomes independent of the number of rent-seekers, dissipation becomes complete in cases where underdissipation prevails in the original model.     

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.     

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.     

Returns to effort in rent-seeking games

In the traditional formulation of rent-seeking games, increasing returns to effort are characterized by an exponent r>1. However, when the value of the rent is normalized to 1, the players’ effort levels A and B will typically be less than 1. Thus, when A<1 and r>1, the value of A ^r decreases as r increases, contradicting the interpretation of r>1 as representing increasing returns to effort. This apparent defect in the mathematization of the problem seems to suggest that a different interpretation of r is required whenever A<1, upsetting the uniformity and elegance of the model. In this short note, we demonstrate that the perceived problem is illusory, and that the usual interpretation of r is satisfactory for all values of A.     

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.