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Stackelberg equilibria with multiple policyholders

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  • Ghossoub, Mario
  • Zhu, Michael B.

Abstract

We examine Pareto-efficient contracts and Stackelberg Equilibria (SE) in a sequential-move insurance market in which a central monopolistic insurer on the supply side contracts with multiple policyholders on the demand side. We obtain a representation of Pareto-efficient contracts when the monopolistic insurer's preferences are represented by a coherent risk measure. We then obtain a representation of SE in this market, and we show that the contracts induced by an SE are Pareto-efficient. However, we note that SE do not induce a welfare gain to the policyholders in this case, echoing the conclusions of recent work in the literature. The social welfare implications of this finding are examined through an application to the flood insurance market of the United States of America, in which we find that the central insurer has a strong incentive to raise premia to the detriment of the policyholders. Accordingly, we argue that monopolistic insurance markets are problematic, and must be appropriately addressed by external regulation.

Suggested Citation

  • Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.
    • Handle: RePEc:eee:insuma:v:116:y:2024:i:c:p:189-201
    DOI: 10.1016/j.insmatheco.2024.02.008
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    References listed on IDEAS

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    Cited by:

    1. Guillermo Alvarez & Ibrahim Ekren & Anastasis Kratsios & Xuwei Yang, 2024. "Neural Operators Can Play Dynamic Stackelberg Games," Papers 2411.09644, arXiv.org.
    2. Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.

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    More about this item

    Keywords

    Optimal (re)insurance; Bowley optima; Stackelberg equilibria; Pareto efficiency; Choquet pricing; Coherent risk measures; Heterogeneous beliefs; Flood risk;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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