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Dynamic Reward Design

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  • Yijun Liu

Abstract

This paper studies a dynamic screening model in which a principal hires an agent with limited liability. The agent's private cost of working is an i.i.d. draw from a continuous distribution. His working status is publicly observable. The limited liability constraint requires that payments remain nonnegative at all times. In this setting, despite costs being i.i.d. and the payoffs being additively separable across periods, the optimal mechanism does not treat each period independently. Instead, it features backloading payments and requires the agent to work in consecutive periods. Specifically, I characterize conditions under which the optimal mechanism either grants the agent flexibility to start working in any period or restricts the starting period to the first. In either case, once the agent begins working, he is incentivized to work consecutively until the end.

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  • Yijun Liu, 2025. "Dynamic Reward Design," Papers 2511.19838, arXiv.org.
    • Handle: RePEc:arx:papers:2511.19838
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    References listed on IDEAS

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    1. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(1), pages 229-265.
    2. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    3. R. Vijay Krishna & Giuseppe Lopomo & Curtis R. Taylor, 2013. "Stairway to heaven or highway to hell: Liquidity, sweat equity, and the uncertain path to ownership," RAND Journal of Economics, RAND Corporation, vol. 44(1), pages 104-127, March.
    4. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel Y., 2020. "The scope of sequential screening with ex post participation constraints," Journal of Economic Theory, Elsevier, vol. 188(C).
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