Full Subgame-Perfect Implementation of Optimal Risk Sharing on an Infinite Menu

Abstract

Can a welfare-maximizing risk-sharing rule be implemented in a decentralized community? We extend the price-and-choose (P&C) mechanism of Echenique and Núñez (2025), in which players sequentially post price schedules and the last mover selects an allocation, from finite choice sets to an infinite risk-sharing menu. Each allocation is modeled as a bounded random vector that redistributes an aggregate loss $X={\sum }_i{X}_i$, and the menu is weak${}^{\ast }$ compact. In subgame-perfect equilibrium, the extended mechanism fully implements the set of allocations that maximize aggregate monetary utility over the admissible menu. The result remains valid when players hold heterogeneous weak${}^{\ast }$-compact credal sets of finitely additive probabilities, or charges, dominated by a reference probability, provided that the induced max-min monetary utilities are uniformly Lipschitz on the menu. We also adapt their first-mover auction to this infinite-menu, multiple-prior environment. Under complete information about all payoff-relevant primitives, the auction admits a symmetric equilibrium that equalizes ex-ante surplus. The resulting procedure therefore achieves optimal and fair risk sharing under heterogeneous priors without trusted third-party enforcement once participants commit to it.

arXiv comment34 pages. An earlier version of this paper circulated under the title "Risk Sharing Among Many: Implementing a Subgame-Perfect and Optimal Equilibrium.''