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Equilibrium in risk-sharing games

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  • Michail Anthropelos
  • Constantinos Kardaras

Abstract

The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. First, it is shown that agents' best response problems have unique solutions. The risk-sharing Nash equilibrium admits a finite-dimensional characterisation and it is proved to exist for arbitrary number of agents and be unique in the two-agent game. In equilibrium, agents declare beliefs on future random outcomes different than their actual probability assessments, and the risk-sharing securities are endogenously bounded, implying (among other things) loss of efficiency. In addition, an analysis regarding extremely risk tolerant agents indicates that they profit more from the Nash risk-sharing equilibrium as compared to the Arrow-Debreu one.

Suggested Citation

  • Michail Anthropelos & Constantinos Kardaras, 2014. "Equilibrium in risk-sharing games," Papers 1412.4208, arXiv.org, revised Jul 2016.
    • Handle: RePEc:arx:papers:1412.4208
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    Cited by:

    1. Michail Anthropelos & Constantinos Kardaras & Georgios Vichos, 2020. "Effective risk aversion in thin risk‐sharing markets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1565-1590, October.
    2. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    3. Anthropelos, Michail & Boonen, Tim J., 2020. "Nash equilibria in optimal reinsurance bargaining," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 196-205.
    4. Michail Anthropelos & Constantinos Stefanakis, 2024. "Continuous-time Equilibrium Returns in Markets with Price Impact and Transaction Costs," Papers 2405.14418, arXiv.org.
    5. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    6. Anthropelos, Michail & Kardaras, Constantinos, 2024. "Price impact under heterogeneous beliefs and restricted participation," Journal of Economic Theory, Elsevier, vol. 215(C).
    7. Wang, Ruodu & Wei, Yunran, 2020. "Characterizing optimal allocations in quantile-based risk sharing," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 288-300.
    8. Maxim Bichuch & Zachary Feinstein, 2020. "Endogenous inverse demand functions," Papers 2012.08002, arXiv.org, revised Apr 2022.

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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