Stackelberg rent-seeking

In this paper I present a formal analysis of rent-seeking games in which the players do not move simultaneously. I consider rent-seeking situations where the players are risk neutral and may value the prize differently. The subgame perfect equilibrium outcome in this Stackelberg game provides several surprising and interesting results. I extend the problem to deal with cases of incomplete information concerning the value a player has for the politically contestable rent.     

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.     

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.     

Rent-seeking with non-identical sharing rules

The primary object of this paper is to examine the role of differential sharing rules within a collective rent-seeking setting on the possible non-existence of Nash equilibrium. Focusing on groups that distribute part of the rent equally among their members and the residual according to relative effort, we show that in rent-seeking societies applying the two polar sharing rules equilibrium never exists. In the general case where groups apply different but not necessarily the polar sharing rules, we study the relationship between group variability in distributing rents and the problem of non-existence of equilibrium in the rent-seeking game.     

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.     

The uniqueness of pure-strategy Nash equilibrium in rent-seeking games with risk-averse players

This article proves that if each player’s measure of absolute risk aversion is nonincreasing in his/her wealth, then there exists a unique pure-strategy Nash equilibrium in the general rent-seeking game, where risk-averse players can coexist with risk-neutral players, attitude toward risk can differ among players, and concave production functions for lotteries are not necessarily the same among players.     

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).

     

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.     

A general analysis of rent-seeking games

In this paper we reconsider the basic model of “efficient rent seeking.” We stress the importance of the shape of the players' reaction curve in order to understand the impact of the technology of rent-seeking on the structure of the outcome of the game. We give a complete characterization of the pure strategy equilibria. Moreover, the possibility of preemption by a Stakelberg leader is discussed according to the nature of the technology of rent-seeking available to the agents.     

Endogenous timing of contest with asymmetric information

Simultaneous moves have been conventionally assumed in modeling rent-seeking competition. However, in reality many forms of contests involve contestants sequentially choosing their effort entries. This study allows agents to choose the timing of their moves before the contest takes place. In contrast to the previous literature, we introduce information asymmetries across agents. We find that in all sequential-move equilibria, the uninformed agent moves first. More generally we show that the order of agents’ moves in a sequential contest is a regularity stemming from information asymmetries. Furthermore, under plausible assumptions, sequential moves Pareto dominate simultaneous moves (from the view point of the players) and also result in lower rent-seeking expenditures. Our result explains the timing pattern in National Presidential Conventions observed from 1948 through 2004. Our result also applies to many other formal or informal institutions, which give rise to sequential contests.     

Veto games: Spatial committees under unanimity rule

There exists a large literature on two-person bargaining games and distribution games (or divide-the-dollar games) under simple majority rule, where in equilibrium a minimal winning coalition takes full advantage over everyone else. Here we extend the study to an n-person veto game where players take turns proposing policies in an n-dimensional policy space and everybody has a veto over changes in the status quo. Briefly, we find a Nash equilibrium where the initial proposer offers a policy in the intersection of the Pareto optimal set and the Pareto superior set that gives everyone their continuation values, and punishments are never implemented. Comparing the equilibrium outcomes under two different agendas – sequential recognition and random recognition – we find that there are advantages generated by the order of proposal under the sequential recognition rule. We also provide some conditions under which the players will prefer to rotate proposals rather than allow any specific policy to prevail indefinitely.     

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.     

General Blotto: games of allocative strategic mismatch

The Colonel Blotto game captures strategic situations in which players attempt to mismatch an opponent’s action. We extend Colonel Blotto to a class of General Blotto games that allow for more general payoffs and externalities between fronts. These extensions make Blotto applicable to a variety of real-world problems. We find that like Colonel Blotto, most General Blotto games do not have pure strategy equilibria. Using a replicator dynamics learning model, we show that General Blotto may have more predictable dynamics than the original Blotto game. Thus, adding realistic structure to Colonel Blotto may, paradoxically, make it less complex.     

Markov perfect equilibrium in multi-period games between sponsor and bureau

We formulate a simple model of the interaction between a sponsor and a bureau. The sponsor sets the bureau's budget while the bureau decides on how much to spend on slack. We compute numerically Markov perfect equilibria of multi-period games where the agents move alternately and apply Markov strategies. Both agents are worse off compared to the one-period game with simultaneous moves. As the discount factors increase, the equilibrium outcome becomes less cooperative in nature.     

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.     

Rent-seeking with scarce talent: A model of preemptive hiring

In a standard rent-seeking contest, players optimally employ resources in an attempt to obtain the rent. Typically, it is assumed that these resources may be hired at any desired level at some exogenous per-unit cost. In practice, these resources often consist of scarce, talented individuals. We model a rent-seeking contest with scarce talent and find that talent scarcity leads to preemptive hiring by the player receiving the larger rent. This player hires all available talent and wins the contest with probability 1. This is true even when the difference in rents is small.     

Rent-seeking with asymmetric valuations

This paper analyzes Tullock's rent-seeking game with asymmetric valuations for a variable range of the returns to scale parameter. A necessary and sufficient condition for a unique pure strategy Nash equilibrium is established. Equilibrium effort and expected profits are determined and subjected to comparative statics analysis. Increasing the underdog's valuation induces both players to increase their efforts. Increasing the favorite's valuation increases his effort but decreases the effort of the underdog. Expected profits increase with a player's valuation but decreases with the valuation of the competitor. The impact of the returns to scale parameter is also analyzed.     

Asymmetric Rent-Seeking with More than Two Contestants

This article considers a rent-seeking model with N asymmetriccontestants. Each contestant may have a different valuation ofthe rent or a different relative ability to win the rent. Oneof the N contestants is selected as the winner based onTullock's probabilistic contest rule with constant returns toscale. A pure strategy Nash equilibrium solution is obtainedand its consequences are investigated.     

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.     

A comparison of rent-seeking models and economic models of conflict

This paper provides a comparative analysis of the basic rent-seeking model and a simple economic model of conflict. Each model is concerned with a game in which players invest resources in pursuit of a prize. The purpose of the analysis is to elucidate structural differences between the two models, and to analyse the consequent behavioral differences and equilibrium outcomes in the two cases. A key finding is that, where such comparisons are possible, the conflict model tends to involve greater relative expenditure on wealth-redistribution activities than does the rent-seeking model.