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Contracting theory with competitive interacting agents

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  • Romuald Elie
  • Dylan Possamai

Abstract

In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as well as impact (positively or negatively) the projects of the other Agents. Considering economic Agents in competition with relative performance concerns, we derive the optimal contracts in both first best and moral hazard settings. The enhanced resolution methodology relies heavily on the connection between Nash equilibria and multidimensional quadratic BSDEs. The optimal contracts are linear and each agent is paid a fixed proportion of the terminal value of all the projects of the firm. Besides, each Agent receives his reservation utility, and those with high competitive appetence are assigned less volatile projects, and shall even receive help from the other Agents. From the principal point of view, it is in the firm interest in our model to strongly diversify the competitive appetence of the Agents.

Suggested Citation

  • Romuald Elie & Dylan Possamai, 2016. "Contracting theory with competitive interacting agents," Papers 1605.08099, arXiv.org.
    • Handle: RePEc:arx:papers:1605.08099
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    Cited by:

    1. Yasuaki Wasa & Ken-Ichi Akao & Kenko Uchida, 2020. "Optimal Dynamic Incentive Contracts between a Principal and Multiple Agents in Controlled Markov Processes: A Constructive Approach," RIEEM Discussion Paper Series 2001, Research Institute for Environmental Economics and Management, Waseda University.
    2. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    3. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.
    4. Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.

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