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A Note on the Multi-Agent Contracts in Continuous Time

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  • Qi Luo
  • Romesh Saigal

Abstract

Dynamic contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information. In this paper, we extend the single-agent dynamic incentive contract model in continuous-time to a multi-agent scheme in finite horizon and allow the terminal reward to be dependent on the history of actions and incentives. We first derive a set of sufficient conditions for the existence of optimal contracts in the most general setting and conditions under which they form a Nash equilibrium. Then we show that the principal's problem can be converted to solving Hamilton-Jacobi-Bellman (HJB) equation requiring a static Nash equilibrium. Finally, we provide a framework to solve this problem by solving partial differential equations (PDE) derived from backward stochastic differential equations (BSDE).

Suggested Citation

  • Qi Luo & Romesh Saigal, 2017. "A Note on the Multi-Agent Contracts in Continuous Time," Papers 1710.00377, arXiv.org, revised Oct 2017.
  • Handle: RePEc:arx:papers:1710.00377
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    File URL: http://arxiv.org/pdf/1710.00377
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    1. repec:cwl:cwldpp:1953rrr is not listed on IDEAS
    2. repec:cwl:cwldpp:1953rr is not listed on IDEAS
    3. Bergemann, Dirk & Strack, Philipp, 2015. "Dynamic revenue maximization: A continuous time approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 819-853.
    4. Fudenberg, Drew & Holmstrom, Bengt & Milgrom, Paul, 1990. "Short-term contracts and long-term agency relationships," Journal of Economic Theory, Elsevier, vol. 51(1), pages 1-31, June.
    5. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 599-617.
    6. Williams, Noah, 2015. "A solvable continuous time dynamic principal–agent model," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 989-1015.
    7. Rogerson, William P, 1985. "Repeated Moral Hazard," Econometrica, Econometric Society, vol. 53(1), pages 69-76, January.
    8. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    9. Oliver D. Hart & Jean Tirole, 1988. "Contract Renegotiation and Coasian Dynamics," Review of Economic Studies, Oxford University Press, vol. 55(4), pages 509-540.
    10. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 957-984.
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