Two-stage team rent-seeking: experimental analysis.

• Author: Cadigan, John

1. Introduction

   In his seminal contribution on rent-seeking activity, Tullock (1967, 1980) develops a model in which players choose effort levels to influence the chance they are awarded a prize. If player effort does not contribute to the value of the prize, rent-seeking effort results in a social welfare loss and can be viewed as inefficient (see also Krueger 1974; Posner 1975). Most research stemming from Tullock's model focuses on contests with simultaneously chosen effort levels and in which the contest prize is awarded to only one contestant or group (see, e.g., Hillman and Katz 1984; Appelbaum and Katz 1987; Snyder 1989; Nitzan 1991; Gradstein 1993; Fullerton and McAffee 1999).

   Many real-world contests are more complicated. For example, congressional elections in the United States typically involve two candidates that receive support from the two major political parties. Both candidates and their parties benefit from a successful bid to capture a seat, and there could be important connections between their effort decisions. A high-quality challenger exerting effort early in an election cycle might receive greater party support by demonstrating an ability to fare competitively in the election. Alternatively, an incumbent's effort might discourage a competitive challenge, freeing party resources for other purposes. In this case, the timing of effort is important, and the contest "prize" is awarded to both the candidate and the candidate's party.

   As another example, many public policy issues are characterized by interest group lobbying from multiple groups on either side of an issue. Successful lobbying by the National Rifle Association, for example, benefits other groups sharing their policy preferences. In a sense, public policy issues motivating lobbying effort can generate public prizes that affect multiple constituencies in different ways. An important aspect of these environments is their team-oriented nature, typically placing groups in one of two camps (for or against free trade, gun control, choice, etc.).

   This paper contributes to the literature on rent-seeking by developing and experimentally testing a two-stage team rent-seeking model in which the contest prize is awarded to each member of the winning team. In one variant of the model, aggregate team effort determines the probabilities associated with the contest outcome. In this case, an individual team member's effort serves as a perfect substitute for the effort of other team members. When effort decisions are sequenced, early movers have the potential to free ride on the effort choices of their later moving teammates. This suggests that lobbying for public policy favors could be subject to the same collective action problems associated with public goods provision. In a second variant of the model, the timing of effort matters. In particular, early effort choices shape the competitive structure of the contest, and in this case early movers cannot free ride on their teammates. The theoretical results also show that effort levels are highest in "competitive contests," with any asymmetries in early effort choices leading to reductions in effort by late-moving teammates.

   The theory is tested by laboratory experimental methods. A few authors have used experimental methods to study rent-seeking (Milner and Pratt 1989, 1991; Shogren and Baik 1991; Davis and Reilly 1998; Onculer and Croson 1998; Potters, de Vries, and Van Winden 1998). Typically, subjects are given an endowment that can be used to invest in a chance to win a prize, with much of the research focusing on symmetric contests with simultaneous effort choices. Generally, subjects tend to overinvest relative to equilibrium predictions, although this tendency diminishes with experience and opportunities for repeated play within a subject group. The paper is also connected to a small but growing literature that examines rent-seeking in more complicated frameworks. Motivated by models of research and development expenditures, Isaac and Reynolds (1988) examine the effects of group size and the degree to which the contest prize is shared on individual investment decisions. They find that a shared prize leads to less investment at the individual level. Anderson and Stafford (2003) examine the effects of cost heterogeneity, group size, and an entry fee on subject participation and expenditures. They find that increases in group size, heterogeneity in costs, and the presence of an entry fee (which makes the decision-making exercise a two-stage game) decrease the number of subjects choosing to participate in the contest. Consistent with theory, increases in group size decrease individual expenditures but increase group expenditures. The use of an entry fee typically reduced individual expenditures, but the results with respect to individual expenditures under cost heterogeneity were mixed. Davis and Reilly (1998) add a "rentdefending buyer" who has a higher value for the contest prize than a group of rent-seeking sellers. In some cases, the buyer bids against one seller who is the winner of a first-stage seller auction, which creates a two-stage game with heterogeneity in the contest prize. Generally, a rent-defending buyer is able to reduce aggregate rent-seeking. In a later paper, Davis and Reilly (2000) examine the effects of experience and adding additional rent-defending buyers, finding that the presence of additional buyers limits efficiency gains. They also find that that experience has limited ability to reduce social costs or the variability of bids.

   Below, I examine rent-seeking in a team environment with a sequential structure and a contest prize that is not excludable among teammates. Consistent with existing research, in all treatments, the experimental results show significant overinvestment relative to the Nash equilibrium prediction. Regarding the qualitative predictions of the model, the results are mixed. Early-moving subjects chose higher effort levels when their late-moving teammate's effort served as a complement rather than a substitute. Effort choices of late movers were not best responses in a game theoretic sense but did display patterns consistent with the shape of the best response functions. Generally, late-moving subjects appear to have responded to the effort levels of their early-moving opponents in the case of substitutable effort levels and to the effort levels of their teammates when effort levels were complements. In contrast to the theoretical predictions, however, early movers did not exploit opportunities to free ride in either single-shot or repeated play treatments, perhaps reflecting some concern for their teammate's payoff.

   The remainder of the paper is organized as follows: Section 2 presents the model and theoretical results; section 3 details the experimental design, procedures, and results; and section 4 concludes.

2. The Model

   Building on the basic structure in Tullock (1980), consider the following two-stage rent-seeking game. In the first stage, two players simultaneously choose effort levels (x and y). These choices are revealed to two second-stage players, who then simultaneously choose effort levels (X and Y). All players are assumed to be risk neutral, and have identical and constant marginal cost of effort (C). The contest prize (B) is awarded to each member of the winning team, with each team consisting of one first-stage and one second-stage player. Effort levels are restricted to be nonnegative. (1) The probability that team X wins the contest (the "contest success function") is

   Px = x + X/ x + X + y + Y.

   Assuming all players act to maximize expected payoffs, the objective functions for the second-stage players (given the first-stage choices of x and y) are

   [U.sub.x](x,X,y,Y) = x + X / x + X + y + Y B - CX

   and

   [U.sub.y](x,X,y,Y) = y + Y / x + X + y + Y B - CY.

   This leads to the following formulas for Nash equilibrium spending in the second stage:

   [X.sup.*] = B/4C - x,

   [Y.sup.*] = B/4C - y.

   Substituting the second-stage equilibrium expenditure formulas into the objective functions of the stage 1 players and simplifying yields:

   [U.sub.x] = B/2 - Cx

   and

   [U.sub.y] = B/2 - Cy.

   This implies the subgame perfect Nash equilibrium to this game has [x.sup.*] = [y.sup.*] = 0, and [X.sup.*] = [Y.sup.*] = B/4C. Essentially, when the contest prize goes to both members of the winning team, irrespective of their relative effort levels, first-stage players are able to shift the burden of effort completely on their teammates. In anticipation of some of the experimental results to follow, note also that the nonnegativity restriction would be binding for stage 2 players if the stage 1 players chose effort greater than B/4C. In this case, although stage 2 players would like to reduce their team's effort, the best they can do is not add to it.

   The results demonstrate that stage 1 players can free ride on the effort of their stage 2 counterparts. In equilibrium, each player equates the marginal benefit and marginal cost of effort. When the contest prize is not excludable between teammates, stage 2 effort levels influence the probability that both members of a team win the prize. Thus, an increase in stage 2 effort reduces the marginal benefit of further effort for both team members. With constant marginal costs, and anticipating the effort level chosen in stage 2, the stage 1 player can free ride, relying on the stage 2 teammate to bring the marginal benefit of effort for both team members into equality with their marginal costs. In a sense, the shared nature of the prize induces a collective action problem similar to those associated with the provision of public goods. Whereas in the public goods case this is typically viewed as inefficient, free riding in the rent-seeking case could be beneficial because it limits wasteful spending.

   One limitation of the previous model is that the timing of effort does not matter--effort exerted in stage 2 is a...