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
Pool Size and the Sustainability of Optimal Risk-Sharing Agreements / Barigozzi, Francesca; Bourlès, Renaud; Henriet, Dominique; Pignataro, Giuseppe. - In: THEORY AND DECISION. - ISSN 0040-5833. - STAMPA. - 82:2(2017), pp. -.273--.303. [10.1007/s11238-016-9573-9]
Pool Size and the Sustainability of Optimal Risk-Sharing Agreements
BARIGOZZI, FRANCESCA;PIGNATARO, GIUSEPPE
2017
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 welfareFile | Dimensione | Formato | |
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