Journal of Economic Behavior Organization Vol. 42 2000 109–124
Allocation efficiency in a competitive bribery game
Derek J. Clark
a,b,∗
, Christian Riis
a,c
a
Department of Economics, NFH, University of Troms ø, N-9037 Tromsø, Norway
b
Norwegian School of Management, BI Troms ø, P.O. Box 973, N-9260 Tromsø, Norway
c
Department of Economics, Norwegian School of Management BI, P.O. Box 580, N-1301 Sandvika, Norway Received 16 June 1999; received in revised form 14 September 1999; accepted 10 November 1999
Abstract
We consider the selection properties of a competitive bribery model in the presence of two types of asymmetry: unevenness between the competitors and unfairness in the contest rules. Only under very
special conditions does the benchmark model yield allocation efficiency; in other cases, the effect on allocation efficiency of making the contest more unfair is ambiguous and parameter specific. We
present conditions under which each result obtains. Our results indicate that it is socially optimal to run an unfair contest in order to redress the allocation inefficiency introduced when contestants
are asymmetric. We show, however, that a selfish, income-maximizing bribee will discriminate in the opposite direction to that which society would prefer. ©2000 Elsevier Science B.V. All rights
reserved.
JEL classification: O17; C72
Keywords: Bribery; Allocation efficiency; Discrimination
1. Introduction
In some countries, it is not uncommon to find government contracts awarded to firms which succeed in bribing a corrupt official. While such corruption has obvious costs, Lien
1986, 1990 has investigated a potential benefit of a competitive bribery procedure as a mechanism for ensuring ex post allocation efficiency; here allocation efficiency is narrowly
defined as the lowest cost firm winning the contract. Two opposing models have been used to model this bribery procedure. Beck and Maher 1986 and Lien 1986 consider the
case in which unsuccessful firms have their bribes refunded; if the highest bribe wins, then this procedure is a first-price sealed bid auction which, as is well known, can possess an
∗
Corresponding author. Fax: +47-77646021. E-mail addresses:
derekcnfh.uit.no D.J. Clark, christian.riisbi.no C. Riis. 0167-268100 – see front matter ©2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 2 6 8 1 0 0 0 0 0 7 7 - 9
110 D.J. Clark, C. Riis J. of Economic Behavior Org. 42 2000 109–124
equilibrium exhibiting ex post allocation efficiency. In Lien 1986, 1990, an alternative set up is used in which all firms, successful or not, forfeit their bribes. Whilst, we prefer
this latter type of model for analyzing corrupt activity, we show that Lien’s assumption that firms are ex ante identical is not innocuous.
In this paper, we look at the role which ‘asymmetry’ plays in the competitive bribery procedure.
1
Following practice in the contest literature see O’Keeffe et al., 1984, we can define two dimensions of asymmetry: i the game may be ‘uneven’ due to the fact
that the contestants are expected to be different; ii an ‘unfair’ contest can arise when the players are treated differently. The game which we specify below, incorporates both of these
elements and investigates the allocation properties which arise in equilibrium. Lien 1986 confines attention to an even and fair contest, whilst Lien 1990 considers an even, unfair
contest. The unique equilibrium of the former is symmetric and hence allocation efficiency is ensured. In the latter paper, one firm is handicapped and must bribe proportionally more
than the opponent in order to win; the equilibrium of this game is not symmetric which leads to the result that ‘the economy may suffer allocation inefficiencies from competitive bribery
procedures, whenever there is some degree of discrimination’ Lien, 1990; 157. In addition, Lien 1990 also shows that increasing the degree of discrimination makes matters worse
i.e. an increase in the probability that the most efficient firm is defeated. Intuitively, these results must obtain since firms are assumed to be ex ante identical and hence a symmetric
equilibrium must result when there is no discrimination among the bribers. Thus, any move away from the symmetry of the no discrimination case must worsen the selection properties
of the bribery procedure.
When all bribes are forfeited, so that losers also bear the full cost of their bribe, one departs from the traditional first-price sealed bid auction procedure and hence, there is in general no
mechanism to ensure allocation efficiency. We show that even a fair bribery procedure leads to inefficiency, except in the very rare case that firms are identical ex ante. Hence, changing
the rules of the game may or may not enhance allocation efficiency, depending on the specific model parameters. Accordingly, increased discrimination in a competitive bribery
procedure may well enhance its selection properties, contradicting Lien’s conclusion.
In the literature, there are two views on corrupt activity.
2
Moralists argue that bribery has no positive effects, whilst reformists take the view that this mechanism may have some
beneficial effects. Among these is allocation efficiency since the most efficient firm should be able to afford the largest bribe and win the contest. We demonstrate that the role of the
bribee is critical in assessing the selection properties of the bribery procedure. It seems likely that the bribee is a selfish actor who desires to maximize his own income in the form
of bribe revenue. We show that this will lead to a direction of discrimination in exactly the opposite direction
to that which society would prefer. Whilst, society would wish for the more efficient firm to be favored — and hence have a greater chance of winning — the
bribee has an incentive to discriminate against this firm in order to even out the contest. This gives both firms an incentive to bribe more; the less efficient firm now has a real possibility
1
The model framework which we use is an all-pay auction under incomplete information; this possesses appli- cations which go beyond bribery. In Clark and Riis 1996, we consider a firm which uses this type of mechanism
to decide which worker to promote to the next level in its hierarchy.
2
See McMullan 1961, Leys 1965 and Heidenheimer 1970.
D.J. Clark, C. Riis J. of Economic Behavior Org. 42 2000 109–124 111
of beating its rival due to the favorable discrimination, whilst the more efficient firm must bribe more to counteract this effect. This result has strong implications for the efficiency of
a competitive bribery procedure. The model and its solution are presented in Section 2. Section 3 examines allocation
