Academic journal article Economic Inquiry

Contests with Stochastic Abilities

Academic journal article Economic Inquiry

Contests with Stochastic Abilities

Article excerpt

I. INTRODUCTION

Many tournaments are characterized by multiple rounds, with or without the elimination of some candidates in earlier stages of the process of determining a final winner. In the political context, election processes that determine party leaders or political leaders more generally consist of multiple contest stages. In the race for the U.S. presidency, several competition stages gradually narrow down the number of competitors. (1) Internal career competition and the selection and succession of CEO's in firms also have features of an elimination tournament in which the number of participants may shrink gradually. (2) Many sports disciplines provide straightforward examples. (3) Also, military conflict usually consists of multiple battles with victory being a function of the outcomes in these battles and with some of the competitors being forced to exit at some stage of the process. Finally, the competition for patents has been termed "racing" by Harris and Vickers (1987) because it can be seen as a multi-battle contest in which the competitor who first accumulates a given number of successes wins.

Contests with multiple rounds or tournaments in which the outcome of previous battles determines whether players are allowed to enter into or win something in later stages of the game have an important holdup feature in common: successful participation in the future stages of the game may require substantial effort and this may make it less attractive to expend effort in preliminary rounds of the game. Similarly, once a player has accumulated a sufficiently large disadvantage in the game, he may simply want to give up, even though success in later rounds may bring him back into play. Returning to a state in which the competition becomes more balanced may not be worth much effort because the economic rents from winning the competition at this state may be dissipated by the efforts expended in the state. Warneryd (1998), McAfee (2000), Muller and Warneryd (2001), Klumpp and Polborn (2006), Konrad (2004), Groh et al. (2003), and Konrad and Kovenock (2005, 2008) illustrate discouragement effects of this type. (4)

The discouragement effect is very strong if the award from winning a competition is admission to an all-pay auction with complete information and no noise. In this contest, which has been characterized by Hillman and Riley (1989) and Baye, Kovenock, and de Vries (1996), the contestant who expends the highest effort wins with probability 1. However, the discouragement effect also emerges in other types of contests, for instance, if winning is a random function of contest efforts, such as in the Tullock (1980) contest, or if the comparison between efforts is disturbed by additive noise as in the tournaments considered by Lazear and Rosen (1981). Some of the contests with multiple rounds cited above consider these latter types of component contests. The discouragement effect of future competition also potentially plays a role in variants of these contests with incomplete information, as in Moldovanu and Sela (2006) or Warneryd (2003). But the combination of repeated interaction and incomplete information raises additional issues.

In this article, we identify and analyze an important reason why the discouragement effect of future conflict may be less severe than current theory would imply. A player's ability, measured, for instance, by his or her cost of expending effort, need not be constant over time, but may be determined as the outcome of a stochastic process. Empirically, the existence of transitory changes in a player's ability is seemingly a very reasonable assumption for all the examples mentioned. Athletes obviously have transitory ups and downs in their ability. The same should apply to managers and workers in firms, to researchers in laboratories and the managers who hire and supervise them, and to politicians and their advisors in the different stages of a campaign. …

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