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Journal Articles Theory and Decision Year : 2017

Pool size and the sustainability of optimal risk-sharing agreements

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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.

Dates and versions

hal-01505776 , version 1 (11-04-2017)

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Francesca Barigozzi, Renaud Bourlès, Dominique Henriet, Giuseppe Pignataro. Pool size and the sustainability of optimal risk-sharing agreements. Theory and Decision, 2017, 82 (2), pp.273-303. ⟨10.1007/s11238-016-9573-9⟩. ⟨hal-01505776⟩
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