the design of rent-seeking competitions: committees, preliminary and final contests

The Design of Rent-Seeking Competitions: Committees, Preliminary and Final ContestsAuthor(s): J. Atsu AmegashieSource: Public Choice, Vol. 99, No. 1/2 (1999), pp. 63-76Published by: SpringerStable URL: http://www.jstor.org/stable/30024509 .

Accessed: 15/06/2014 19:51

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Springer is collaborating with JSTOR to digitize, preserve and extend access to Public Choice.

http://www.jstor.org

This content downloaded from 195.78.108.147 on Sun, 15 Jun 2014 19:51:13 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=springer

http://www.jstor.org/stable/30024509?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Public Choice 99: 63-76, 1999. © 1999 Kluwer Academic Publishers. Printed in the Netherlands.

63

The design of rent-seeking competitions: Committees, preliminary and final contests*

J. ATSU AMEGASHIE 671 Highview Road, Pickering, Ontario, Canada LIV 4W2

Accepted 21 May 1997

Abstract. The paper examines the common practice in multi-contest rent-seeking competitions, where "finalists" are selected, based on rent-seekers' efforts in a preliminary contest. We find that for any single-contest design, rent-seeking expenditures could be reduced by introducing a preliminary contest, if the marginal returns to rent-seeking effort in the preliminary contest is sufficiently low. In addition to other reasons, the paper argues that this may explain why such multi-contest designs are common. We argue that rent-seeking expenditure in the preliminary stage represents the cost of reducing the number of contestants. We also find that the practice of setting a higher "quality" standard in the final contest than the "quality" standard in the preliminary contest reduces rent-seeking waste. We derive an expression for the optimal number of finalists; under certain conditions we find that the optimal number of finalists is directly proportional or equal to the square root of the number of potential contestants. Finally, we show that whether rent-seeking expenditures rise or fall when the rent is awarded by a committee instead of a single administrator depends on the sensitivity of the committee relative to that of the single administrator.

1. Introduction

Since Tullock's (1967) seminal work, there has been an explosion of literature on rent-seeking. It now known that several factors affect rent-seeking expenditures; some of these are the number of winners (Clark and Riis, 1996), the attitude of rent-seekers towards risk (Hillman and Katz, 1984), the number of rent-seekers and the rent-giver's sensitivity to seeking expenditures (Tullock, 1980),' the degree of asymmetry of seekers' valuations Hillman and Riley, 1989), the timing of moves (Leininger, 1993), and the number of rent-givers Congleton, 1984).

To the best of my knowledge, there has not been any research to examine a very common design of rent-seeking competitions. In most rent-seeking competitions, there is (are) usually a preliminary contest(s) and a final contest. The finalists are chosen after competing in the preliminary contest. Recently,

* My thanks are due to Dan Usher for his help and encouragement and to an anonymous

referee for his comments. I also thank Samuel Darku, Ed Kutsoati, Kwasi Ofori-Yeboah, John Spicer, Wisdom Tettey, and the Adinkrah Family for their immense support.



64

Baye, Kovenock, and de Vries (1993), tried to answer the following question: why do politicians frequently "announce" that they have narrowed down a set of potential recipients of a "prize" to a slate of finalists?2 They show that narrowing the number of potential contestants may maximise a politician's bribes. However, in their model, there is no preliminary competition to the determine who the finalists should be. Michaels (1988, section 1) follows a similar approach.

Higgins, Shughart, and Tollison (1985) examine a two-stage rent-seeking competition. In the first-stage the rent-seekers, playing a game in mixed strategies,

decide whether or not to incur an exogenous sunk cost. They refer to this as an entry fee. Each of the active rent seekers then choose a level of effort in the final stage. The final number of contestants (i.e., the active rent seekers) in the second-stage is determined such that expected profits are zero. Obviously, their main objective was to get round the unpleasant result of rent over-dissipation (see also Tullock's 1985 comment on their paper). Also, the competition in the first stage is different from the preliminary competitions examined in this paper since rent-seeking expenditures in the preliminary stage are exogenous.3 Indeed, their model was not intended to answer the above question posed by Baye, Kovenock, and de Vries (1993). Commenting on the number of contestants for a monopoly prize, they write (p. 255):

"... It is unsatisfactory to imagine, for example, that the franchisor sets the number of contestants. One could then forsee that rent-seeking would arise to influence the permissible number of bidders and this merely moves the rent-seeking dissipation question one step back".

But it may be the case that the number of finalists is set by the franchisor or by a higher authority (say a politician) who would then delegate the job of choosing the finalists and awarding the prize to his subordinates (e.g., bureaucrats). So

although it may be unsatisfactory, for whatever reason, to imagine this, it may be worthwhile to examine this practice, given that it is common. This

paper examines this practice. We examine a two-stage rent-seeking game in which rent-seekers play Tullock's (1980) game in both stages. Indeed, the

paper moves the rent-dissipation question one step back. However, we do not consider rent-seeking to influence the permissible number of bidders; rent-

seeking (in the first stage) only determines which of the players should belong to the permissible number of bidders. We compare rent-seeking expenditures in this two-stage design with expenditures in competitions with only one stage. The paper could be seen in two ways: (i) as an attempt to examine the efficiency of multi-stage rent-seeking contests, in terms of the level of socially wasteful expenditures, relative to single-stage contests and/or (ii) to argue that



65

the reason why a group of potential contestants is sometimes reduced to a set of finalists is because this results in lower rent-seeking expenditures compared to single-stage competitions.

There are, however, in my opinion, other reasons why multi-stage competitions are common. They may be used to reduce the cost of organising rent-seeking competitions. The rent giver(s) may want a process which selects the eventual winner after a thorough examination of his "quality" (e.g., com-

petence). To do this, they may have to conduct interviews, inspections, etc. Inspections may require members of the award committe to schedule an appointment with each applicant, undertake travel, and so on. Time, money, and resources may not permit a "thorough" examination of all contestants. So, for example, there is a preliminary contest in which all contestants are only interviewed (with no inspection of plant, equipment, etc), and a final stage in which a few finalists are interviewed and inspected. Even in competitions, which take the form of only interviews, it may be necessary to have a preliminary interview where all applicants are interviewed for, say twenty minutes, and a final competition in which a few applicants, chosen after the preliminary interview, are interviewed for, say an hour. There may not be enough resources to interview every applicant for an hour.

Another reason why multi-stage competitions are common may be to make the process of contesting for the prize free from arbitrary "disqualifications" or exclusion of some contestants. To see this, note that one of the main policy prescriptions for reducing rent-seeking expenditures is to reduce the number of potential applicants. However, without any preliminary competition to determine which applicants should be excluded, the only option available is an arbitrary or random process (which takes no account of the abilities of the contestants) to exclude some of the contestants. This arbitrary process may be considered unfair.4, 5 But if the reason why multi-stage designs are used is to make the process (of reducing the number of contestants) fair, one would expect the number of finalists to be set at the smallest level possible (say two). Our analysis, however, shows that although reducing the number of finalists leads to a fall in rent-seeking expenditures in the final stage, it could lead to an increase in rent-seeking expenditures in the preliminary stage. Hence, given that a preliminary competition (in the interest of "fairness") is necessary, the optimal number of finalists need not be a corner solution.

Related to the above reasons, is the fact that reducing the number of contestants based on zero information may not be optimal. If all rent-seekers were identical and if this were known by the franchisor, then there would be no need for any competition. The optimal policy, assuming that the rent has to be awarded, would be to choose randomly from the pool of contestants. But in the real world, the applicants may not be identical. A random selection



66

process which reduces the number of applicants, without regard to their abilities, may imply that a high proportion of highly competent applicants may be excluded. A preliminary competition may reduce the risk of excluding such applicants. Even if rent-seeking expenditures, like lobbying, are wasteful, they may convey some information about the relative abilities of applicants. For example, in a competition for a monopoly franchise, firms with lower costs and hence higher expected profits will tend to lobby more, since they have higher valuations of the franchise.

Let me digress for a moment to consider the following question: can a rent- giver who wishes to eliminate "wasteful" rent-seeking expenditures achieve this objective by giving the impression that he is not sensitive to such expenditures? If he can perfectly discriminate between wasteful expenditures and valuable expenditures, then it is obvious that he can achieve this objective. However, it may be the case, in spite of his desire, that he can only identify such wasteful expenditures imperfectly. He may, for example, be vulnerable to some misleading arguments or information (data) that may be presented by some of the rent-seekers to prove their competence and justify their claim to the prize. From this brief discussion, it is not hard to imagine that a rent-

giver's sensitivity to rent-seeking expenditures will depend on his knowledge of the relevant issues, his personality (e.g., he may be a fastidious person), the extent to which he thinks the reduction of rent-seeking expenditures is an

important objective, etc. Unless otherwise stated, we shall consider the number of finalists chosen

from the preliminary competition as exogenous. Note, however, that although the number of finalists is exogenous, the process by which they become finalists is endogenous; that it is, they are chosen as finalists based on their rent-seeking expenditures in a preliminary competition. I assume, unless otherwise stated, that all rent-seeking expenditures are socially wasteful. I also assume that all agents have complete information.

The paper is organised as follows: in the next section, I describe a method for choosing the finalists in the preliminary contest. Section 3 examines rent-

seeking expenditures in a two-stage design relative to the single-stage design. In Section 4, I compare rent-seeking expenditures when the rent is awarded by a committe instead of a single administrator. Section 5 concludes the paper.

2. Choosing the finalists

It is necessary to find a method for choosing the finalists in any multi-contest design. It may be interesting to note that any method used to choose the winners or losers in multi-winner or multi-loser contests as in Clark and Riis (1996) and Usher (1995) respectively, could be used, with appropriate



67

modifications, to determine the finalists and vice-versa. As Clark and Riis (1996) note, there is no unique way for picking out several winners. Similarly, there is no unique way for picking the finalists. For example, in Clark and Riis (1996), k > 1, winners are to be chosen from N (> k) identical players.6 They employ the following method for choosing the winners: The players make one rent-seeking contribution. The winners are then determined sequentially. The first winner is determined by using the probability distribution which arises after the rent-seeking outlays of all N players are collected. The first winner is then eliminated and the second winner is determined by using the probability distribution which arises when the outlay of the first winner is excluded. This process continues until all k winners are determined. This method could be used to examine the model presented in this paper. However, I shall use another method, which I think is more analytically tractable and which seems to be consistent with most competitions. The method is the following. Suppose that f > 1 finalists are to be chosen from N (> f) contestants in the preliminary contest. The contestants are divided into f groups each with N/f players,7 where there is a preliminary competition for the members of each group. A finalist is then chosen from each group. This method is common in most competitions. Athletes at the Olympics run in preliminary competitions in different groups and then finalists are chosen from each group. The NBA playoffs is played in groups, from which two finalists are determined. Teams in the World Cup in Soccer are divided into six preliminary groups of four each. Applicants for jobs are interviewed in groups; for example those whose surnames begin with A-D, E-H, and so on.8 After interviewing applicants in each group, it is not unreasonable to assume that the interviewers may have determined which applicants in the group should be shortlisted. Finally, in the American television quiz competition, Jeopardy, finalists, from different groups, are chosen from preliminary competitions. While the method chosen is somewhat different from what happens in the real world, it is nonetheless a good approximation.

It is interesting to note that this method, applied to a multi-winner contest, gives the same results obtained by Clark and Riis (1996). That is, there is full rent dissipation when N is infinitely large (contrary to Berry's (1993) result) and a change in the number of winners leads to an ambiguous effect on aggregate rent-seeking expenditures. To see this, note that the i-th contestant, competing with (N/k-1) identical and risk-neutral players in his group, chooses his rent-seeking expenditure zi to maximise piV(k)-zi, where pi is the probability that the i-th contestant is the winner in his group and V(k) is each contestant's valuation of each of the k identical prizes.9 Using, as in Clark and Riis (1996), Tullock's (1980) probability function with constant returns to scale, each contestant's expenditure, in a symmetric Cournot-Nash equilib-



68

rium, is given by z = [(N/k-1)/(N/k)2]V(k). Total rent-seeking expenditures Z = Nz = [k(N-k)/N]V(k). Clearly as N approaches infinity Z approaches kV(k), which confirms Clark and Riis (1996) result of full rent-dissipation. Also the sign of dZ/dk is indeterminate unless a function for V(k) is specified. For example, if as in Berry (1993), V(k) = V/k, then dZ/dk < 0, where we have equality when N approaches infinity (as in Clark and Riis).

3. A multi-stage rent-seeking contest

As in the previous sections, consider N identical and risk-neutral agents competing for a monopoly prize. Suppose that 1 < f < N contestants are chosen in a preliminary competition to contest in a final stage. The contestants are divided into f groups with N/f contestants in each group. A finalist is chosen from each group. It is conceivable that the administrator of the preliminary competition may be different from the administrator of the final competition. Using Tullock's (1980) probability function, let a > 0 and b > 0 be the

parameters which capture the sensitivity of the administrators in the preliminary and final competitions respectively.10 Let xil and x i2 be the expenditure of the i-th seeker in the preliminary stage and in the final stage (given that he is a finalist) respectively. The probability of being a finalist is given by pil(a,xil,xji) = (xil)a/[(xil)a + (N/f - 1)(xjl)a], where xjl is the mean expenditure of the (N/f-1) contestants in the i-th player's group in the preliminary contest. The probability of winning the prize given that the i-th contestant is a finalist is given by pi2(b,xi2,Xj2) = (Xi2)b/[(Xi2)b + (f-1)(Xj2)b], where xj2 is the mean expenditure of the other (f-1) contestants in the final contest. Let V be each seeker's common valuation of the prize. I shall solve for the

subgame perfect pure-strategy (Nash) equilibrium of this game by backwards induction. Given f contestants in the final stage, the expenditure by each contestant, in a symmetric Cournot-Nash equilibrium, is x2 = [b(f-1)/f2]V, which implies that aggregate rent-seeking expenditure in the final stage is T2 = fx2 = [b(f-1)/f]V. The equilibrium expected payoff is E2 = (1/f)V-x2 = [f - b(f-1)]V/f2. Since the analysis is restricted to pure strategies, we require a positive expected payoff in the second stage. If the expected payoff in the second stage is zero or negative, then there will be no rent-seeking expenditures in the first stage since any expenditure will lead to a negative expected equilibrium payoff. But "no expenditure" cannot be an equilibrium since each contestant has the incentive to spend a small but positive amount in the first

stage in order to be the only finalist and hence win the prize with certainty. Obviously, this leads to the problem that bogged reseachers for sometime (see Leininger, 1993, page 1, and the references cited therein). I ignore this problem by assuming that b < f/(f-1); that is E2 > 0.11



69

In the first stage, the i-th contestant chooses xil, given the outlay of the other (N/f-1) contestants in his group, to maximise

Eil = Pil ()E2 - Xil (1)

In a symmetric Cournot-Nash equilibrium, this gives xl = a[(N/f-1)/(N/f)2]E2. Aggregate rent-seeking expenditure in the first stage is given by T1 = Nx1 = a[f(N-f)/N]E2. The expected payoff in this subgame perfect equilibrium is E1 = (f/N)E2 - xl, which is non-negative if a < N/(N-f). Given that reducing the number of contestants will necessarily result in efforts to belong to the permissible number of bidders (as the above quote in Higgins et al. (1985) indicates), we may consider this first-stage rent-seeking expenditure as the cost of reducing the number of contestants. Thus, the standard policy recommendation that the number of contestants must be

reduced may not be implemented costlessly. It follows, as will be shown shortly, that it is not always optimal to reduce the number of contestants.

The grand rent-seeking expenditure is T = T1 + T2. It follows immediately that dT/da > 0 but dT/db < 0 (given f < N). Hence, contrary to the standard result in the rent-seeking literature, an increase in the rent-giver's sensitivity (i.e., b) to rent-seeking expenditures leads to a fall in aggregate rent-seeking expenditures. This result is due to the dynamic nature of this game. While an increase in b leads to increase in rent-seeking expenditures in the final competition, this conversely leads to a fall in rent-seeking expenditures in the preliminary stage (holding "a" fixed), because the increase in expenditures in the final stage reduces the expected payoff for any given number of finalists. Hence the seekers take this reduced payoff, E2 into account in the first stage. In our model, the fall in the first-stage aggregate expenditure outweighs the rise in second-stage expenditure (given an increase in b). It follows, given dT/da > 0 and dT/db < 0, that in a two-stage game, T is lower when a < b than when a > b. A related implication of this analysis is the following paradoxical result: if the administrator in charge of the preliminary contest is sensitive to (socially wasteful) rent-seeking expenditures (i.e., a > 0), then it may be welfare-improving for the administrator in charge of the final contest to have some sensitivity to rent-seeking expenditures (b > 0), rather than no sensitivity (b = 0). This is clearly an example of second-best theory; if an irremovable distortion exists (i.e., a > 0), then it may be optimal to depart from the first-best rule (b = 0) in a related activity.

Note that while a fall in f results in a fall in rent-seeking expenditures in the final stage, it could lead to an increase in rent-seeking expenditures in the preliminary stage. That is, the sign of dT1/df = -a[f2(1-b)+bN]V/Nf2 is indeterminate. The intuition behind this result follows immediately from the analysis in the preceeding paragraph. A fall in the number of finalists leads



70

to a fall in the equilibrium probability (f/N) of being a finalist, which should lead to a fall in each contestant's rent-seeking expenditure in the first stage. However, there is an opposing effect because, a fall in the number of finalists leads to a rise in the equilibrium expected payoff, E2, when a contestant is a finalist; this leads to a rise in each contestant's first-stage rent-seeking expenditure. The balance of these opposing effects is ambiguous.

So far I have assumed that rent-seeking expenditures are socially wasteful.12 If we assume that rent-seeking expenditures have some social value, then the result that a < b results in a smaller rent-seeking expenditure than a > b may have some practical relevance. Recently, Gottinger (1996) has defined the returns to scale parameter (i.e., a and b) as the rent-giver's sensitivity to quality (assuming that expenditures are measured in quality units). He then asserts that the higher is the rent-giver's scrutiny of quality, the greater his sensitivity to quality. We could hypothesise further that the higher is the quality standard set in a given stage, the higher is the degree of scrutiny (i.e., more thorough interview, inspection etc), and hence the higher is the rent-giver's sensitivity to quality. As was discussed in section 1, the "quality" standard set in the preliminary stage is usually lower than the "quality" standard in the final stage. That is, the examination in the preliminary stage is less thorough than the one in the final stage. Hence, even if the administrator in both stages is the same person (or group), the sensitivity to quality will be lower in the

preliminary stage than the final stage, because the quality standard is lower in the preliminary stage and thus the degree of scrutiny or examination is also lower. In other words a < b. Hence the practice of setting a higher quality standard in the final stage of a multi-stage competition, may reduce social waste. Waste in this case refers to the expenditure of the unsuccessful contenders, since their quality bids may have no further use. The expenditure of the winner is not wasted though.

In what follows, we return to our assumption that all rent-seeking expenditures are socially wasteful. To compare rent-seeking expenditures in this

two-stage design to rent-seeking expenditures in the single-stage design, I shall assume that the sensitivity of the rent giver in the second stage of the

two-stage design is the same as the sensitivity of the rent-giver in the single stage design. That is, the single-stage game and the final stage are synony- mous. In other words, given only a final stage, will the introduction of a

preliminary stage reduce or increase rent-seeking expenditures? Thus given identical and risk-neutral N contenders in a single-stage game, aggre-



71

gate rent-seeking expenditure, in a Cournot-Nash equilibrium, is S = b[(N-1) /N]V. Now S > T, if

f(I - b) + b < b/a. (2)

T > S when (2) is not satisfied. That is, it is not optimal to reduce the number of contestants (by introducing a preliminary competition). From (2), the following results are obtained:

(i) If a = b = 1, then T = S

(ii) If a > 1 and b = 1, then T > S

(iii) If a = b < 1, then T > S

(iv) If a = 1 and b < 1, then T > S

(v) If a = b > 1, then T < S

(vi) If a = 1 and b > 1, then T < S

(vii) If a < 1 and b = 1, then T < S

(viii) If a < 1 and b < 1, then T < S, if b is sufficiently greater than a.

Inspection of (i) through (viii) shows that if a and b are sufficiently high [i.e., case (v)] or b is sufficiently greater than a, then this two-stage design results in lower rent-seeking expenditures than the single-stage design. To illustrate case (viii), suppose that a = 0.2 and b = 0.8, then T < S so long as 1 < f < 16. If a = 0.1 and b = 0.5, then T < S if 1 < f < 9. The above results imply that for any single-stage design, we can reduce rent-seeking expenditures by introducing a preliminary stage, if the sensitivity of the administrator in this stage is sufficiently low. It also follows, given our earlier discussion on rent- seeking expenditures which take the form of quality bids, that introducing a preliminary stage with a very low quality standard may be welfare improving. This low quality standard could take the form of asking potential contestants, say job applicants, to send their curriculum vitae and nothing else. Only the finalists chosen will be asked to send references, take an aptitude test, attend an interview, etc.

We now determine the value of f which minimises rent-seeking expenditures. Assuming continuity of f, the optimal value of f satisfies dT/df =

-[af2(1-b)+bN(a-1)]V/Nf2 = 0, which gives f* = mN1/2, where m = [b(a- 1)/a(b-1)]l1/2. For a real value of f* and to satisfy the second-order condition for a minimum (i.e., d2T/df2 > 0), we require a > 1 and b > 1. It follows that when the sensitivity of the rent givers to rent-seeking expenditures is very high, the optimal number of finalists is directly proportional to the total number of rent-seekers, N. Indeed, in our model, the optimal number of finalists is directly proportional to the square root of N and it is equal to the square root



72

of N, if a = b > 1. Note that m < 1, when a < b. The reason why an increase in the number of contestants requires an increase in the number of finalists is the following: An increase in N results in an increase in rent-seeking expenditures in the preliminary stage. To counteract this effect, it is necessary to increase the number of finalists; this leads to an increase in the rent-seeking expenditures in the final stage, and an increase in the equilibrium probability of being a finalist (f/N). But it also leads to a reduction in the equilibrium expected payoff, E2. It is this latter effect which leads to the reduction in the

first-stage rent-seeking expenditures required to counteract the increase in

rent-seeking expenditures due to a rise in N. df*/dN gives the exact amount by which the number of finalists should change in response to a change in N (in order to minimise rent-seeking expenditures).

As shown in section 2, an increase in the number of winners in a single- stage contest leads to a fall in rent-seeking expenditures, given that a fixed rent of size, V, is distributed equally among k winners and that N is finite (i.e., dZ/dk < 0, given V(k) =V/k). I shall briefly consider the effect of increasing the number of winners on rent-seeking expenditures, T, in this two-stage game, given V(k) = V/k and finite N. Suppose that k (< f), winners will be chosen from the f finalists in the final stage. Obviously total rent-seeking expenditures in the final stage will be Z2 = bk(f-k)V(k)/f = b(f-k)V/f (see section 2). The expected payoff in the final stage is E2' = (k/f)V(k) - Z2/f =

[f - b(f-k)]V/f2. Therefore, rent-seeking expenditure in the first stage is Z1 = a[f(N - f)/N]E2'. It follows that d(Z1 + Z2)/dk = b[a(N-f)/N - 1]V/f < 0, if a < N/(N-f). Hence total rent-seeking expenditure is non-increasing in k, given that for a non-negative expected payoff (in the first-stage), we require a < N/(N-f). So in this two-stage game, increasing the number of winners will (at best) lead to a fall in rent-seeking expenditure and (at worst) keep rent-seeking expenditures unchanged, given that a fixed rent is distributed

equally among the winners.

4. Committees and rent-seeking expenditures

In this section, I consider the following question: Given two administrators in this two-stage contest, is it optimal for both administrators, acting as a committee, to determine the finalists in the first stage and also jointly determine the winner in the final stage, instead of each administrator acting in only one

stage? That is, which design leads to lower rent-seeking expenditures? Con-

gleton (1984) shows, in a single-stage design, that rent-seeking expenditures are lower when the rent is awarded by a committee than when it is awarded by a single administrator. In what follows, I shall show that the relative magnitude of expenditures could go either way depending on the committee's sensitivity



73

to rent-seeking relative to the single administrator. Consider a single-stage competition with N risk-neutral and identical seekers. Suppose that the rent will be awarded by a two-member committee. Let pia be the probability that the committee member whose sensitivity to rent-seeking expenditures is "a" selects the i-th seeker as the winner and let xia be the rent-seeking expenditure by the i-th seeker to influence this committee member. Let Pib and xib be similarly defined for the committee member whose sensitivity is captured by the parameter b.13 I assume that if the committee members select different contestants, then this is resolved by a random process which selects one of the two contestants (chosen by the members). Hence, the probability that the i-th contestant wins the prize is given by Pi = Pia Pib +(1/2)Pia(1-Pib)+(1/2)(1-Pia)Pib. Each contestant chooses xia and xib to maximise PiV - xia - Xib. Using, as before, Tullock's (1980) probability function for each committee member, the equilibrium symmetric rent-seeking expenditure for each contestant is given by xa = (a/2)[(N-1)/N2]V and xb = (b/2)[(N-1)/N2]V. As one would expect, more rent-seeking effort will be directed towards the committee member with the higher sensitivity to rent-seeking expenditures. Aggregate rent-seeking expenditure is N(xa+xb) = c[(N-1)/N]V, where c = (a+b)/2 could be defined as the average sensitivity of the committee to rent-seeking expenditures. It follows that, in a single-stage design, if an administrator with a higher sensitivity forms a committee with another administrator with a lower sensitivity, then rent-seeking expenditures will be higher than if the rent had been awarded by only the administrator with the lower sensitivity. The reverse case leads to Congleton's (1984) conclusion. This result is intuitively appealing . For the sake of argument, consider a rent which is awarded by an administrator who is not sensitive to rent-seeking expenditures. Obviously, there will be no rent-seeking expenditures. Suppose instead that this administator is joined by r other administrators and that at least of one them is sensitive (no matter how small) to rent-seeking expenditures, then obviously there would be some rent-seeking expenditures directed towards these members of the committee.

Extending the above result of the committee in the single-stage design to the two-stage design is straightforward. Since the sensitivity of the committee is the average of the sensitivities of its members, we just have to replace a and b with c in the expression for T to obtain the level of aggregate rent-seeking expenditures when the committee acts in both stages. Recall that in section 3, we found that a lower sensitivity in the first stage and a higher sensitivity in the final stage (i.e., a < b) leads to lower rent-seeking expenditures than the reverse case (a > b). Indeed, the sensitivity (i.e., a) of the administrator in the preliminary stage should be as low as possible and that of the administrator in the final stage (i.e., b) should be as high as possible. Thus, if a < b, then the introduction of a committee increases sensitivity in the preliminary stage and



74

reduces sensitivity in the final stage. It follows that when each administrator is in charge of only one stage and the administrator with the higher sensitivity determines the winner in the final stage while the one with the lower sensitivity determines the finalists in the preliminary stage, this leads to a smaller rent- seeking expenditure than the case of both administrators acting as a committee in each stage. If the sensitivity of the administrators are the same, then whether a committee acts in both stages or single administrators acts in each stage has no effect on the relative magnitude of rent-seeking expenditures.

5. Conclusion

This paper has examined the practice of selecting finalists in rent-seeking competitions, based on seekers' efforts in a preliminary competition. The analysis was restricted to a two-stage competition. That is, there is only one preliminary competition. We provide a very simple and tractable method for choosing the finalists (or for choosing the winners in multi-winner competitions). We find that if the sensitivity of rent-givers is very high in both stages or the sensitivity of the administrator in the final stage is sufficiently higher than the sensitivity of the administrator in the preliminary stage, then the two-stage design results in lower rent-seeking expenditures than the single-stage design. Indeed, the model shows that in a dynamic game, the standard result that an increase in the sensitivity of rent-givers results in an increase in rent-seeking expenditures is not necessarily correct. Given this, we obtain the paradoxical result that if the administrator in the preliminary stage is sensitive to socially wasteful expenditures, then it may be welfare improving to have an administrator in the final stage who is also sensitive to rent-seeking expenditures rather than one who is not sensitive to rent-seeking expenditures. Extending Gottinger's (1996) interpretation of the rent-giver's sensitivity to the efforts of contestants, we find that when the efforts of seekers have some social value, then the practice of setting a higher quality standard in the final stage and a lower quality standard in the preliminary stage reduces rent-seeking waste.

The paper also shows that when the sensitivity of the rent-givers is sufficiently high, then the number of finalists which minimises rent-seeking expenditures is equal to a given proportion, m, of the square root of the number of contestants. This implies that the optimal number of finalists as a proportion of the number of contestants will tend to be small as the number of contestants gets large. This seems to be consistent with multi-stage competitions which involve a large number of contestants.

We also find that a rent awarded by a committee may result in higher rent- seeking expenditures than a similar rent awarded by a single administrator, if



75

the average sensitivity (however this is measured) of the committee is higher than sensitivity of the single administrator.

As discussed in the introduction, reasons like the need to use a "fair" and information-based method to reduce the number of contestants and the lower costs of organisation may explain why multi-stage (or specifically two-stage) designs are common. But it is not unreasonable to think that two-stage designs (instead of single stage designs) are used because they may lead to lower rent- seeking expenditures. Rent-seeking expenditure in the preliminary stage may be considered as the cost of reducing the number of contestants. Therefore the standard policy prescription that the number of contestants must be reduced may not be implemented costlessly. By comparing the single-stage design with the two-stage design, the paper shows that the benefit of reducing the number of contestants may outweigh the cost. Indeed, all these factors, taken together, provide a strong justification for the use of multi-stage designs.

Notes

1. There has been an explosion of literature since Tullock (1980) presented his game-theoretic rent-seeking model. Indeed, this paper and most of the references cited herein are based on Tullock (1980).

2. For example, as noted by Baye, Kovenock, and de Vries (1993), the International Olympic Committee selected six cities as "finalists" for the 1996 Summer Olympics: Belgrade, Manchester, Toronto, Melbourne, Athens, and Atlanta.

3. Hartwick (1982) has a similar model. In a prototype development contest, an exogenous amount, c dollars is sunk in a preliminary contest, with an exogenous probability, p of making the shortlist. The winner is then selected at random from those who make the shortlist. Hence, there is no rent-seeking contest in the final stage and the expenditure in the preliminary stage, as in Higgins, Shughart, and Tollison (1985), is exogenous.

4. The use of the word "rigging" in the title of the paper by Baye, Kovenock, and de Vries (1993) suggests that arbitrary or random exclusion of some contestants may be considered unfair.

5. Even if the "fairness" objective is ignored, it is not possibe to reduce the number of contestants without giving rise to rent-seeking of the type refered to in the above quote in Higgins et al. (1985).

6. Note that while all k winners receive a prize in a multi-winner contest, not all the finalists may receive a prize.

7. For simplicity, I assume that N/f is an integer. Note that, given f > 1, N/f cannot be an integer if N is a prime number. If N is not a prime number, then there exists an f which makes N/f an integer.

8. Even if this alphabetical grouping process is not used, a given number of applicants is interviewed in a day.

9. To see why each contestant's valuation of the prize may depend on the number of winners, consider a contest in which a rent of size, V, is distributed equally among the k winners (i.e., V(k) = V/k).

10. It is also possible for the same administrator to have different sensitivities in different stages.



76

11. Indeed, we also need to assume that "a" is not greater than N/(N-f). This will be obvious in a moment.

12. For an interesting discussion of the welfare implications of rent-seeking expenditures, or better still, directly unproductive profit-seeking activities, see Bhagwati (1982).

13. Our result remain unchanged if rent-seekers had to influence both members simultaneously by spending say X which is then observed by both members of the committee.

References

Baye, M., Kovenock, D. and de Vries, C.G. (1993). Rigging the lobbying process: An appli- cation of the all-pay auction. American Economic Review 83: 289-294.

Bhagwati, J. (1982). Directly unproductive profit-seeking (DUP) activities. Journal of Political Economy 90: 988-1002.

Berry, S.K. (1993). Rent-seeking with multiple winners. Public Choice 77: 437-443. Clark, D.J. and Riis, C. (1996). A multi-winner nested rent-seeking contest. Public Choice 87:

177-184. Congleton, R. (1984). Committees and rent-seeking effort. Journal of Public Economics 25:

197-209. Gottinger, H.W. (1996). Competitive bidding for research. Kyklos 49: 439-447. Hartwick, J.M. (1982). Efficient prizes in prototype development contests. Economics Letters

10: 375-379. Higgins, R.S., Shughart II, W. F. and Tollison, R.D. (1985). Free entry and efficient rent-

seeking. Public Choice 46: 247-258. Hillman, A.L. and Katz, E. (1984). Risk-averse rent-seekers and the social cost of monopoly

power. Economic Journal 94: 104-110. Hillman, A.L. and Riley, J.G. (1989). Politically contestable rents and transfers. Economics

and Politics 1: 17-39. Leininger, W. (1993). More efficient rent-seeking - A Miinchhausen solution. Public Choice

75: 43-62. Michaels, R. (1988). The design of rent-seeking competitions. Public Choice 56: 17-29. Tullock, G. (1967). The welfare cost of tariffs, monopoly and theft. Western Economic Journal

5 (June): 224-232. Tullock, G. (1980). Efficient rent-seeking. In J.M. Buchanan, R.D. Tollison and G. Tullock.

Toward a theory of the rent-seeking society. Texas A&M University Press. Tullock, G. (1985). Back to the bog. Public Choice 46: 259-263. Usher, D. (1995). Victimization, rent-seeking and just compensation. Public Choice 83: 1-20.



the design of rent-seeking competitions: committees, preliminary and final contests

Documents