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Theory and Decision

, Volume 82, Issue 2, pp 273–303 | Cite as

Pool size and the sustainability of optimal risk-sharing agreements

  • Francesca Barigozzi
  • Renaud Bourlès
  • Dominique Henriet
  • Giuseppe Pignataro
Article

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

Optimal risk-sharing agreement Loss-mitigating actions Repeated interactions Collectively optimal vs Nash behaviors 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Francesca Barigozzi
    • 1
  • Renaud Bourlès
    • 2
  • Dominique Henriet
    • 2
  • Giuseppe Pignataro
    • 1
  1. 1.Department of EconomicsUniversity of BolognaBolognaItaly
  2. 2.Centrale Marseille (Aix-Marseille School of Economics), CNRS & EHESSMarseille Cedex 20France

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