Incorporating policymaker costs and political competition into rent-seeking games.

• Author: Godwin, R. Kenneth
• Position: Tullock's model

We incorporate policymaker costs of supplying rents and variable intensities of competition among rent seekers into the standard rent-seeking game. By incorporating these aspects, the game has greater verisimilitude to the lobbying process. The first aspect captures the fact that in rent-seeking contests there is a positive probability that neither firm will obtain the rent. The second aspect captures the fact that firms seeking different rents still must compete for policymakers' resources. We find that lobbying expenditures, rent-seeking profits, and rent dissipation depend on the intensity of competition and the value of the rent relative to policymaker costs. For example, if the value of the rent is sufficiently high relative to policymakers' costs, an increase in the intensity of political competition will increase lobbying expenditures; otherwise, expenditures fall as competitive intensity increases. In addition, the model establishes pure-strategy equilibria with underdissipation where only mixed-strategy equilibria exist in the standard model.

JEL Classification: D72, H42, L51

1. Introduction

   Rent seeking in politics involves agents who lobby policymakers for potential benefits. In a seminal contribution, Tullock (1980) modeled rent seeking as a lottery game. A major weakness of Tullock's game was that it lacked verisimilitude to actual rent seeking because it omitted politics. The absence of politics meant that the game essentially assumed that there are no costs to the policymakers of supplying rents. But as Tollison (1997) and others have pointed out, these costs are not zero, and the politics surrounding the policy decision influence the pattern of lobbying and the rent-seeking outcome. In this paper we address two aspects of those politics: the costs to policymakers of supplying rents and the variable intensity of political competition among a given number of rent seekers. Including these aspects increases the similarity of the game to actual rent-seeking situations and makes clearer the incentives to rent seekers.

   Costs to supplying rents arise due to various constraints. Legislators must build coalitions, acquire parliamentary rights, maintain a positive image, and service constituent interests. Policymakers in agencies must follow procedural rules, submit to congressional oversight and budgeting, pass OMB reviews, and so forth. Lower policymaker costs should increase the effectiveness of lobbying, and this should attract greater lobbying efforts among rent seekers. (1) Increasing policymaker costs makes lobbying less effective. Indeed, because of these costs policymakers often turn away lobbies empty-handed. In short, policymakers have constraints that affect the policies they design, and this affects lobbying expenditures (Dougan and Snyder 1993). This paper introduces policymaker costs in monetary units, such that they are comparable to the value of the rent and rent-seeking expenditures.

   Political competition among rent seekers also influences the rent-seeking outcome. Competition traditionally has been modeled by varying the number of rent-seeking agents (actual or potential) or their relative lobbying expenditures (e.g., Posner 1975; Rogerson 1982; Sun and Ng 1999). Competition can vary, however, even among a given number of rent seekers and for a given profile of expenditures. For example, two agents may lobby a policymaker for the same unique and exclusive political good. Then one agent directly opposes the other and only one agent can win the good. Alternatively, the same two agents may lobby a policymaker for two separate political goods. In that case, the agents oppose each other only indirectly. This situation is frequent in politics as rent-seeking agents compete for space on the political agenda, for policymakers' time, and for portions of a particular government budget. In this situation, success by one agent does not necessarily result in failure by the other, but it does lower the probability that the other agent will succeed. Competition is more intense in the first example, even though the examples involve the same number of finns. Industrial organization economists have shown that a single parameter can determine incumbent firms' competition in price and quantity regardless of the number of firms present. (2) This paper introduces rent-seeking competition analogously, allowing a parameter to alter the competitiveness of the rent-seeking game among a fixed number of firms.

   We incorporate monetized policymaker costs and the political competition parameter into the success probabilities of the standard rent-seeking game. The resulting model is a game in which the agents' simultaneous maximization of expected net returns (or profits) determines a Nash equilibrium in their expenditures. Incorporating politics into the standard game makes the game more accurate because equilibrium and comparative statics depend in part on the politics of the rent-seeking contest. More specifically, increasing political competition decreases rent-seeking expenditures unless the value of the rent is sufficiently large relative to policymaker costs; and dissipation rates are lower than in previous research because of policymaker costs. Furthermore, under increasing returns to expenditures there is a unique pure-strategy equilibrium with underdissipation of rents, unlike the standard game, which has stochastic mixed-strategy equilibria with overdissipation occurring about half the time.

   Intuitively, in the model incorporating politics, rent seekers will avoid competition with each other, search for low-cost providers of political goods, and generally avoid overdissipation. With such implications, our model extends the Tullock game in a political-economic sense, reaching more empirically reasonable results than previous models.

2. The Standard Rent-Seeking Model (3)

   Following Tullock (1980), consider two agents competing for a private good with expenditures [R.sub.1] and [R.sub.2] and success probabilities

   [P.sub.1] = [R.sup.[sigma].sub.1]/[[R.sup.[sigma].sub.1] + [R.sup.[sigma].sub.2]] and [P.sub.2] = [R.sup.[sigma].sub.2]/[[R.sup.[sigma].sub.1] + [R.sup.[sigma].sub.2]]

   where [P.sub.1] + [P.sub.2] = 1, which implies that one agent must win. [sigma] indicates "returns to scale" in expenditures; for example, if [sigma] > 1, then an increase in [R.sub.i], ceteris paribus, causes a more than proportionate increase in agent i's probability of winning. (4) If [sigma] is the same for both agents, then the game is "unbiased": the agents are equally suited to rent seeking. Tullock reasoned that if [sigma] = 2 and n = 2 in an unbiased game, then combined symmetric expenditures would equal the value of the prize. Following convention, we call this "exact dissipation." But if [sigma] > 2 for two agents (or [sigma] > n/(n - 1) for n agents), Tullock reasoned that total spending in an unbiased game will always exceed the value of the rent, and this usually will occur in biased games. This result is "overdissipation" and forms the basis of Tullock's social waste argument.

   Many game theorists were attracted to Tullock's curious result, and most of the rent-seeking models that followed attempted to rule out overdissipation in equilibrium. New contributions emerged with increasing complexities, such as open-ended sequential games, uncertain prizes, risk-averse rent seekers, budget constraints, entry conditions, and various sharing rules for groups of winners. As a consequence, this literature formalized and generalized Tullock's reasoning. (5) By incorporating policymaker costs and political competition into the basic model, this paper formalizes the idea that rent seeking takes place within a political context that influences patterns of rent seeking and the outcomes observed (Tollison 1997). The model suggests a more politically realistic solution to overdissipation.

3. Rent Seeking with Policymaker Costs and Political Competition

   In previous formulations of rent-seeking contests, players' success probabilities are related only to their relative lobbying expenditures, regardless of the value of [sigma]. It has been noted in several places (e.g., Baye, Kovenock, and de Vries 1994; Che and Gale 1997) that if [sigma] is finite, then the game is a lottery; and if [sigma] [right arrow] [infinity], then the game is an all-pay auction. For any finite value of or, the chances of player i's success increase directly with expenditures [R.sub.i]. In the lottery, the winner is selected according to probabilities; in the all-pay auction the winner is the highest bidder. Such an approach assumes a costless political process. In contrast, define N [member of] (0, [infinity]) as the monetized disutility to the policymaker of providing the rent. Thus conceived, the policymakers' costs may be influenced by any number of institutional factors. For instance, N may depend on the political body that is lobbied. For middle-level regulatory waivers, there may be a small number of policymakers involved, little formal oversight, and negligible lobbying opposition--in this case N may be close to zero. Alternatively, for major legislative changes in which a winning coalition must form against powerful opposition and re-election constraints, N may be very high. Policymaker costs also could depend on the selection of a voting rule--majority rule would have a lower N than would a supermajority rule. Stronger checks and balances also affect policymaker costs: for U.S. style judicial review, N may be moderate, but for Swiss style legislative referendum, N may be much higher (Moser 2000; Spindler and de Vanssay 2003). Individual policymakers can have different values of N, depending on their regulatory/ parliamentary power over a policy (Denzau and Munger 1986; Grier and Munger 1991). Public perception may help to determine N if it involves a policy that would attract substantial negative media attention to the policymaker(s).

   Consider...