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Optimal sharing, equilibria, and welfare without risk aversion

Author

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  • Jean-Gabriel Lauzier
  • Liyuan Lin
  • Ruodu Wang

Abstract

We analyze Pareto optimality and competitive equilibria in a risk-exchange economy, where either all agents are risk seeking in an expected utility model, or they exhibit local risk-seeking behaviour in a rank-dependent utility model. A novel mathematical tool, the counter-monotonic improvement theorem, states that for any nonnegative allocation of the aggregate random payoff, there exists a counter-monotonic random vector, called a jackpot allocation, that is componentwise riskier than the original allocation, and thus preferred by risk-seeking agents. This result allows us to characterize Pareto optimality, the utility possibility frontier, and competitive equilibria with risk-seeking expected utility agents, and prove the first and second fundamental theorems of welfare economics in this setting. For rank-dependent utility agents that are neither risk averse or risk seeking, we show that jackpot allocations can be Pareto optimal for small-scale payoffs, but for large-scale payoffs they are dominated by proportional allocations, thus explaining the often-observed small-stake gambling behaviour in a risk sharing context. Such jackpot allocations are also equilibrium allocations for small-scale payoffs when there is no aggregate uncertainty.

Suggested Citation

  • Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2024. "Optimal sharing, equilibria, and welfare without risk aversion," Papers 2401.03328, arXiv.org, revised Dec 2024.
  • Handle: RePEc:arx:papers:2401.03328
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    References listed on IDEAS

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    Cited by:

    1. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures," Papers 2412.00655, arXiv.org.
    2. Peng Liu & Tiantian Mao & Ruodu Wang, 2024. "Quantiles under ambiguity and risk sharing," Papers 2412.19546, arXiv.org.

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