Multi-Battle Contests

Konrad, Kai A.; Kovenock, Dan

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Multi-Battle Contests

CEPR Discussion Paper No. 5645

35 Pages Posted: 19 Jul 2006

See all articles by Kai A. Konrad

Kai A. Konrad

Max Planck Institute for Tax Law and Public Finance; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute for Economic Research); IZA Institute of Labor Economics

Dan Kovenock

Chapman University - Economic Science Institute; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: April 2006

Abstract

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there.

Keywords: All-pay auction, contest, race, conflict, multi-stage, R&D, endogenous uncertainty, preemption, discouragement

Suggested Citation: Suggested Citation

Konrad, Kai A. and Kovenock, Daniel, Multi-Battle Contests (April 2006). CEPR Discussion Paper No. 5645, Available at SSRN: https://ssrn.com/abstract=918292