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arXiv · 2505.04122

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

Michiko Ogaku
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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.

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Michiko Ogaku. 2025-05-07. Full Subgame-Perfect Implementation of Optimal Risk Sharing on an Infinite Menu. https://arxiv.org/abs/2505.04122

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