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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.

Year: 2009

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oai:CiteSeerX.psu:10.1.1.135.2383

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