Optimal sharing, equilibria, and welfare without risk aversion

Jean-Gabriel Lauzier, Liyuan Lin and Ruodu Wang

Papers from arXiv.org

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.

Date: 2024-01, Revised 2024-12
New Economics Papers: this item is included in nep-mic, nep-rmg and nep-upt
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Citations: View citations in EconPapers (2)

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