Optimal sharing, equilibria, and welfare without risk aversion

2024-01-06

AI Summary

This paper addresses the impact of empirically observed heterogeneity in individual risk attitudes—particularly loss-domain risk-seeking—on risk-sharing mechanisms, challenging the conventional assumption of universal risk aversion. Method: We develop a general equilibrium model of risk exchange without presupposing risk aversion, employing inverse-monotonic optimization, rank-dependent utility, and expected utility frameworks to characterize Pareto-optimal allocations, existence of competitive equilibria, and validity conditions for the First and Second Welfare Theorems. Contribution/Results: We provide the first rigorous proof of both welfare theorems under pure risk-seeking preferences. Introducing the “jackpot allocation” concept, we identify a scale-dependent mechanism: jackpot allocation is Pareto optimal for small gains but dominated by proportional allocation for large ones—unifying explanations of the disposition effect and small-stakes gambling. Our results resolve a fundamental tension between behavioral evidence and standard general equilibrium theory.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Analyzes optimal risk sharing with realistic risk attitudes
• Explores Pareto optimality and welfare theorems empirically
• Generalizes expected utility for mixed risk preferences

Innovation

• Analyzes risk sharing with realistic attitudes
• Generalizes expected utility for diverse behaviors
• Uses counter-monotonic improvement theorem