Abstract
Contests have different, sometimes quite complex, organisational structures. In particular, while most of the existing literature focusses on simultaneous contests, multistage contests are also quite frequently encountered. This paper seeks to provide a rationale for the latter by endogenising the choice of a contest structure, which is made by an organiser of a contest interested in maximising the efforts expended by the contenders.
The authors are indebted to two referees and the editor of this Journal for their valuable comments and suggestions.
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References
Being an ubiquitous social phenomenon, contests have been extensively studied in a variety of other contexts as well, including labour market reward structures (see e.g., Rosen, 1986; Glazer and Hassin, 1988), conflict theory (Hirshleifer, 1991; Skaperdas, 1992, 1995), and political competition (Hillman and Ursprung, 1988; Skaperdas and Grofman, 1995 ).
Tullock’s (1980) seminal paper that predicts the amount expended in a contest to be almost equal to the value of the rent has provoked much research interest. Different comparative statics results pertaining to the contestants’ outlay have been derived in the literature since then. For instance, it turns out that the outlay is larger when the contestants are similar (with regard to their abilities, tastes, etc.) and if their number is big (Hillman and Riley 1989; Gradstein 1995 ). For the effect of risk aversion see Hillman and Katz (1984) and Konrad and Schlesinger (1997). Total outlay is smaller when the contestants first choose an order of play and then carry out the actual rent seeking game (see Morgan, 1998, and references therein); or when collective benefits exist (Nitzan, 1991 ).
For instance, in monopolistic competition, technological change may change the equilibrium structure in an industry and in particular decrease the equilibrium number of firms. A series of such changes may cause a stepwise reduction in the equilibrium number of firms. The process of adjustment to the new equilibrium industry structure often has the feature of a contest: firms make sunk investments in RandD and/or in excess capacity (Thum, 1995) in order to increase their chances of surviving, and these costs cannot be recovered even if the firm has to exit. The contest nature of dynamic competition has been recognised in the RandD literature, and in the literature on network externalities (e.g., Besen and Farrell 1994 ). If the technology shocks are relatively small, we observe a series of contests with the winning firms in each stage qualifying for the next contest stage — the structure is similar to a T-contest. With drastic shocks, the number of contest stages is much smaller and, if one big shock yields the new long term industry equilibrium structure, the contest resembles an S-contest.
Likewise, in political situations, multistage contests are very common, either explicitly as in the case of candidate selection in the primaries and the subsequent presidential elections, or implicitly, when only individuals elected for an office are qualified to run for a higher office.
In the related context of internal labour markets, the literature on tournaments (see e.g., Lazear and Rosen (1981) and Green and Stokey (1983)) has examined the optimal incentive schemes to ensure a maximal effort. In contrast to the rent seeking models, this literature typically invokes the assumption that the amount to be divided among the contestants is affected by their effort, which is non-observable or non-verifiable.
Three other contributions belong to this research agenda. Lazear (1996, pp. 127–33) considers two-stage contests that differ with respect to the number of matches played. In particular, he compares knock-out systems and all-play-all contests. The number of contest stages is exogenous, but contestants differ with respect to ability. Gradstein (1998) compares simultaneous and pairwise multistage contests with a specific probability-of-winning function addressing the issue of timing of effort exertion which is absent in this paper, but without taking up the general problem of contest design, namely, what contest structure is optimal when the class of admissible contests contains all multistage (and single-stage) contests. Amegashie (1998) studies shortlisting of contestants, whereby a contest can only include a subset of potential candidates who compete for the right to enter the contest prior to the contest itself, focusing on the conditions under which shortlisting can reduce/increase the amount of resources spent. Thus, shortlisting constitutes a special case of our multistage contest with only two stages. This restricted framework, however, is unable to address the issue of the optimal number of stages in a contest, which is a central element of the contest design here.
We assume in this paper that the contest rules, specifying in particular the winning odds, are exogenously given and focus exclusively on contest matching structure.
This implicitly assumes that the marginal cost of effort is 1; the results can be easily extended, however, to allow any constant marginal cost.
See Skaperdas (1996) for its axiomatisation.
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Gradstein, M., Konrad, K.A. (2001). Orchestrating Rent Seeking Contests. In: Lockard, A.A., Tullock, G. (eds) Efficient Rent-Seeking. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5055-3_34
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DOI: https://doi.org/10.1007/978-1-4757-5055-3_34
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