Pool size and the sustainability of optimal risk-sharing agreements

Francesca Barigozzi, Renaud Bourlès (), Dominique Henriet and Giuseppe Pignataro

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Abstract: We study a risk-sharing agreement where members exert a loss-mitigating action which decreases the amount of reimbursements to be paid in the pool. The action is costly and members tend to free-ride on it. An optimal risk-sharing agreement maximizes the expected utility of a representative member with respect to both the coverage and the (collective) action such that efficiency is restored. We study the sustainability of the optimal agreement as equilibrium in a repeated game with indefinite number of repetitions. When the optimal agreement is not enforceable, the equilibrium with free-riding emerges. We identify an interesting trade-off: welfare generated by the optimal risk-sharing agreement increases with the size of the pool, but at the same time the pool size must not be too large for collective choices to be self-enforcing. This generates a discontinuous effect of pool size on welfare.

Keywords: Collectively optimal; Loss-mitigating actions; Optimal risk-sharing agreement; Repeated interactions (search for similar items in EconPapers)
Date: 2017-02
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Citations: View citations in EconPapers (1)

Published in Theory and Decision, 2017, 82 (2), pp.273-303. ⟨10.1007/s11238-016-9573-9⟩

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Related works:
Journal Article: Pool size and the sustainability of optimal risk-sharing agreements (2017)
Working Paper: Improving Compliance With Preventive Care: Cooperation in Mutual Health Insurance (2011)
Working Paper: Risk-sharing with self-insurance: the role of cooperation (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01505776

DOI: 10.1007/s11238-016-9573-9

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