Round-Robin Tournaments with Limited Resources

25 Pages Posted: 8 Aug 2017

See all articles by Dmitry Dagaev

Dmitry Dagaev

National Research University Higher School of Economics

Andrey Zubanov

University of Wisconsin-Madison - Department of Economics

Date Written: August 8, 2017

Abstract

We propose a theoretical model of a round-robin tournament with limited resources motivated by the fact that in a real-world round-robin sport tournament participating teams are sometimes forced to distribute their effort over an extended period. We assume that the participating teams have a limited amount of effort that must be distributed between all matches. We model the outcome of each match as a first-price sealed-bid auction. Results are aggregated after all matches are played with respect to the number of wins. The teams distribute their effort striving to maximize the expected payoff at tournament completion. For a three team tournament, we describe the set of all subgame perfect Nash equilibria in pure strategies. For tournaments with a relatively low first prize, we found two types of equilibria: ‘effort-saving’ and ‘burning out’, both leading to unequal payoffs. In contrast, for tournaments with a large first prize a limited budget of effort, in general, does not allow for the first or the last move advantage to be exploited.

Keywords: Contest, Round-Robin Tournament, Limited Resources, First-Price Auction, First-Mover Advantage

JEL Classification: C73, D44, Z20

Suggested Citation

Dagaev, Dmitry and Zubanov, Andrey, Round-Robin Tournaments with Limited Resources (August 8, 2017). Higher School of Economics Research Paper No. WP BRP 171/EC/2017, Available at SSRN: https://ssrn.com/abstract=3015255 or http://dx.doi.org/10.2139/ssrn.3015255

Dmitry Dagaev (Contact Author)

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

Andrey Zubanov

University of Wisconsin-Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706
United States

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