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Computing an Optimal Contract in Simple Technologies

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  • Yuval Emek
  • Michal Feldman

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.

Suggested Citation

  • Yuval Emek & Michal Feldman, 2007. "Computing an Optimal Contract in Simple Technologies," Discussion Paper Series dp452, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp452
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    References listed on IDEAS

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    1. Eyal Winter, 2004. "Incentives and Discrimination," American Economic Review, American Economic Association, vol. 94(3), pages 764-773, June.
    2. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    3. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    4. Patrick Legros & Steven A. Matthews, 1993. "Efficient and Nearly-Efficient Partnerships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 599-611.
    5. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 433-446.
    6. Roland Strausz, "undated". "Moral Hazard in Sequential Teams," Papers 001, Departmental Working Papers.
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