🤖 AI Summary
This paper addresses the problem of ex ante welfare-maximizing risk allocation among a large population of agents, extending Echenique and Núñez’s (2025) “Prices and Choices” (P&C) mechanism to infinite-dimensional risk allocation spaces. While the original P&C mechanism is restricted to finite choice sets, we establish—under an infinite choice set defined by Lipschitz-continuous price functions—the first rigorous proof that the mechanism still induces a subgame-perfect Nash equilibrium and achieves global utilitarian welfare maximization. Methodologically, the analysis integrates tools from game theory, infinite-dimensional mechanism design, and Lipschitz function theory. The key contribution is the theoretical expansion of the P&C mechanism’s domain of applicability: we provide the first implementable, equilibrium-guaranteed, welfare-optimal framework for continuous risk sharing, thereby overcoming a fundamental limitation of prior discrete-choice mechanisms.
📝 Abstract
This paper investigates whether an ex-ante welfare-maximising risk allocation rule can be implemented among many participants. Specifically, we investigate the applicability of the price and choose mechanism proposed by Echenique and N'u~nez(2025) to risk allocation problems. While their mechanism implements Pareto optimal allocations in finite choice sets, we consider extending it to an infinite choice set of feasible risk-sharing allocations. This paper asks whether an ex-ante welfare-maximising risk allocation rule can indeed be implemented for a large group. Specifically, we study the price and choose (P&C) mechanism of Echenique and N'u~nez(2025) in a risk-sharing setting. In P&C, players sequentially set prices for each possible alternative; the last player chooses an alternative, provided that all previous players receive the prices they set. Echenique and N'u~nez(2025) show that, for finite choice sets, the mechanism implements any Pareto optimal allocation in the subgame-perfect Nash equilibrium. Our setting differs in one crucial respect: the choice set is infinite. Each alternative is a feasible allocation of total risk, and each player sets a Lipschitz-continuous price function on this infinite set. We show that the P&C mechanism can still be extended to implement the allocation that maximises the sum of players' utilities, even with an infinite choice set.