OPTIMAL MULTI‐AGENT PERFORMANCE MEASURES FOR TEAM CONTRACTS

Hyeng Keun Koo, Gyoocheol Shim and Jaeyoung Sung

Mathematical Finance, 2008, vol. 18, issue 4, 649-667

Abstract: We present a continuous‐time contracting model under moral hazard with many agents. The principal contracts many agents as a team, and they jointly produce correlated outcomes. We show the optimal contract for each agent is linear in outcomes of all other agents as well as his/her own. The structure of the optimal contract strikingly reveals that the optimal aggregate performance measure in general can be orthogonally decomposed into two statistics: one is a sufficient statistic, and the other a nonsufficient statistic. As a consequence, the optimal aggregate performance measure in general is not a sufficient statistic, unless the principal is risk neutral. We further discuss agents' optimal effort choices using a “quadratic‐cost” example, which also strikingly suggests that team contracts sometimes provide lower‐powered effort incentives than individually separate contracts do.

Date: 2008
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