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Computing an Optimal Contract in Simple Technologies

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  • Yuval Emek

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  • Michal Feldman

    ()

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    Abstract

    We study an economic setting in which a principal motivates a team of strategic agents to exert costly effort toward the success of a joint project. The action taken by each agent is hidden and affects the (binary) outcome of the agent's individual task stochastically. A Boolean function, called technology, maps the individual tasks' outcomes into the outcome of the whole project. The principal induces a Nash equilibrium on the agents' actions through payments that are conditioned on the project's outcome (rather than the agents' actual actions) and the main challenge is that of determining the Nash equilibrium that maximizes the principal's net utility, referred to as the optimal contract. Babaioff, Feldman and Nisan [1] suggest and study a basic combinatorial agency model for this setting. Here, we concentrate mainly on two extreme cases: the AND and OR technologies. Our analysis of the OR technology resolves an open question and disproves a conjecture raised in [1]. In particular, we show that while the AND case admits a polynomial-time algorithm, computing the optimal contract in the OR case is NP-hard. On the positive side, we devise an FPTAS for the OR case, which also sheds some light on optimal contract approximation of general technologies.

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    Bibliographic Info

    Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp452.

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    Length: 23 pages
    Date of creation: May 2007
    Date of revision:
    Handle: RePEc:huj:dispap:dp452

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    1. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    2. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    3. Patrick Legros & Steven Matthews, 1993. "Efficient and nearly efficient partnerships," ULB Institutional Repository 2013/7040, ULB -- Universite Libre de Bruxelles.
    4. Eyal Winter, 2003. "Incentives and Discrimination," Discussion Paper Series dp313, The Center for the Study of Rationality, Hebrew University, Jerusalem.
    5. Manishi Prasad & Peter Wahlqvist & Rich Shikiar & Ya-Chen Tina Shih, 2004. "A," PharmacoEconomics, Springer Healthcare | Adis, vol. 22(4), pages 225-244.
    6. Roland Strausz, . "Moral Hazard in Sequential Teams," Papers 001, Departmental Working Papers.
    7. Mookherjee, Dilip, 1984. "Optimal Incentive Schemes with Many Agents," Review of Economic Studies, Wiley Blackwell, vol. 51(3), pages 433-46, July.
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