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Nash Equilibria in Optimal Reinsurance Bargaining

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  • Michail Anthropelos
  • Tim J. Boonen

Abstract

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents' strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents' strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents' bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.

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  • Michail Anthropelos & Tim J. Boonen, 2019. "Nash Equilibria in Optimal Reinsurance Bargaining," Papers 1909.01739, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1909.01739
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    3. Lu-Ping Liu & Wen-Sheng Jia, 2021. "An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game," Mathematics, MDPI, vol. 9(5), pages 1-14, February.
    4. Chen, Yanhong & Cheung, Ka Chun & Zhang, Yiying, 2024. "Bowley solution under the reinsurer's default risk," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 36-61.

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