Optimal Timing in Competition for Advantage: A Two‐Stage Contest

Konstantinos Protopappas

Journal of Public Economic Theory, 2025, vol. 27, issue 3

Abstract: We study a two‐stage contest between two players who differ in ability, with a prize awarded in the second stage. In the first stage, players compete, and the winner enjoys a reduced effort cost in the second stage. The second‐stage contest is simultaneous, while the first‐stage contest can be simultaneous or sequential. We investigate how a sequential first stage affects the catching‐up and discouragement effects between players. Additionally, we explore the optimal first‐stage timing structure of contest designers with different objectives, that is, maximizing effort in the second stage, total effort across both stages, or the winner's total effort. Interestingly, a designer focused on maximizing second‐stage effort prefers a simultaneous first‐stage contest, contrary to the conventional intuition that the stronger player should lead.

Date: 2025
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