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Dynamic risk-sharing with two-sided moral hazard

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  • Zhao, Rui R.

Abstract

In this paper I study a class of repeated two-sided moral hazard problems with discounting. I consider two agents who are involved in multiperiod, and possibly infinite-horizon, contractual relationships. In every period, the agents simultaneously take hidden actions, each of which independently affects the distribution of a separate random public signal. The realizations of the public signals jointly determine the output of a perishable final good, which the agents consume. This abstract framework can be used to analyze contractual relations within a variety of institutions, such as partnership firms, households, or cooperatives, in which bilateral moral hazard is an essential feature. I examine the nature of Pareto optimal contracts in this environment that respect both technological and informational constraints. After establishing the existence of optimal contracts, I show that every continuation contract of an optimal contract is itself optimal. Using this recursive property, next I derive a partial, but fairly general, characterization of optimal consumption allocations. It is an equation that links the ratio of marginal utilities of the agents in the current period to the same ratio in the next period. Moreover, optimal contracts imply that the sequence of ratios of marginal utilities in each period is a submartingale. I provide sufficient conditions for the submartingale to converge. Finally, using this result, I identify conditions under which one agent receives all surplus in the long run.
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  • Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
  • Handle: RePEc:eee:jetheo:v:136:y:2007:i:1:p:601-640
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    Cited by:

    1. Keiichi Hori & Hiroshi Osano, 2013. "Managerial Incentives and the Role of Advisors in the Continuous-Time Agency Model," Review of Financial Studies, Society for Financial Studies, vol. 26(10), pages 2620-2647.
    2. Mele, Antonio, 2014. "Repeated moral hazard and recursive Lagrangeans," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 69-85.
    3. Karel Janda, 2006. "Lender and Borrower as Principal and Agent," Working Papers IES 2006/24, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2006.
    4. Michail Anthropelos, 2012. "The Effect of Market Power on Risk-Sharing," Papers 1206.0384, arXiv.org, revised May 2016.
    5. Philipp Renner & Karl Schmedders, 2017. "Dynamic Principal–Agent Models," Working Papers 203620456, Lancaster University Management School, Economics Department.

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