Reward Design in Risk-Taking Contests

SIAM Journal on Financial Mathematics, forthcoming

16 Pages Posted: 9 Mar 2021 Last revised: 6 Nov 2021

See all articles by Marcel Nutz

Marcel Nutz

Columbia University

Yuchong Zhang

University of Toronto - Department of Statistics

Date Written: February 5, 2021

Abstract

Following the risk-taking model of Seel and Strack, n players decide when to stop privately observed Brownian motions with drift and absorption at zero. They are then ranked according to their level of stopping and paid a rank-dependent reward. We study the problem of a principal who aims to induce a desirable equilibrium performance of the players by choosing how much reward is attributed to each rank. Specifically, we determine optimal reward schemes for principals interested in the average performance and the performance at a given rank. While the former can be related to reward inequality in the Lorenz sense, the latter can have a surprising shape.

Keywords: Stochastic contest, Stackelberg game, optimal stopping

Suggested Citation

Nutz, Marcel and Zhang, Yuchong, Reward Design in Risk-Taking Contests (February 5, 2021). SIAM Journal on Financial Mathematics, forthcoming, Available at SSRN: https://ssrn.com/abstract=3799336 or http://dx.doi.org/10.2139/ssrn.3799336

Marcel Nutz

Columbia University ( email )

Yuchong Zhang (Contact Author)

University of Toronto - Department of Statistics ( email )

700 University Ave.
Toronto, Ontario M5S 1Z5
Canada

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