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

Michiko Ogaku

Papers from arXiv.org

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 N\'u\~nez (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.

Date: 2025-05, Revised 2026-08
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-rmg
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