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Hail Mary Pass: Contests with Stochastic Progress

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  • Chang Liu

Abstract

This paper studies the equilibrium behavior in contests with stochastic progress. Participants have access to a safe action that makes progress deterministically, but they can also take risky moves that stochastically influence their progress towards the goal and thus their relative position. In the unique well-behaved Markov perfect equilibrium of this dynamic contest, the follower drops out if the leader establishes a substantial lead, but resorts to "Hail Marys" beforehand: no matter how low the return of the risky move is, the follower undertakes in an attempt to catch up. Moreover, if the risky move has a medium return (between high and low), the leader will also adopt it when the follower is close to dropping out - an interesting preemptive motive. We also examine the impact of such equilibrium behavior on the optimal prize allocation.

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  • Chang Liu, 2023. "Hail Mary Pass: Contests with Stochastic Progress," Papers 2305.07218, arXiv.org.
    • Handle: RePEc:arx:papers:2305.07218
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    1. Christopher Harris, 1993. "Generalized Solutions of Stochastic Differential Games in One Dimension," Papers 0044, Boston University - Industry Studies Programme.
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