Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914359813341184 |
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| author | Ogaku, Michiko |
| author_facet | Ogaku, Michiko |
| contents | Can a welfare-maximising risk-sharing rule be implemented in a large, decentralised community? We revisit the price-and-choose (P&C) mechanism of Echenique and Núñez (2025), in which players post price schedules sequentially and the last mover selects an allocation. P&C implements every Pareto-optimal allocation when the choice set is finite, but realistic risk-sharing problems involve an infinite continuum of feasible allocations.
We extend P&C to infinite menus by modelling each allocation as a bounded random vector that redistributes an aggregate loss $X=\sum_i X_i$. We prove that the extended mechanism still implements the allocation that maximises aggregate (monetary) utility, even when players entertain heterogeneous credal sets of finitely additive probabilities (charges) dominated by a reference probability $\mathbb{P}$. Our credal sets are weak$^{\ast}$-compact and are restricted so that utility functionals are uniformly Lipschitz on the feasible set.
Finally, we pair P&C with the first-mover auction of Echenique and Núñez (2025), adapted to our infinite-menu, multiple-prior environment. Under complete information about players' credal sets, the auction equalises the surplus among participants. The result is a decentralised, enforcement-free procedure that achieves both optimal and fair risk sharing under heterogeneous priors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium Ogaku, Michiko Theoretical Economics Can a welfare-maximising risk-sharing rule be implemented in a large, decentralised community? We revisit the price-and-choose (P&C) mechanism of Echenique and Núñez (2025), in which players post price schedules sequentially and the last mover selects an allocation. P&C implements every Pareto-optimal allocation when the choice set is finite, but realistic risk-sharing problems involve an infinite continuum of feasible allocations. We extend P&C to infinite menus by modelling each allocation as a bounded random vector that redistributes an aggregate loss $X=\sum_i X_i$. We prove that the extended mechanism still implements the allocation that maximises aggregate (monetary) utility, even when players entertain heterogeneous credal sets of finitely additive probabilities (charges) dominated by a reference probability $\mathbb{P}$. Our credal sets are weak$^{\ast}$-compact and are restricted so that utility functionals are uniformly Lipschitz on the feasible set. Finally, we pair P&C with the first-mover auction of Echenique and Núñez (2025), adapted to our infinite-menu, multiple-prior environment. Under complete information about players' credal sets, the auction equalises the surplus among participants. The result is a decentralised, enforcement-free procedure that achieves both optimal and fair risk sharing under heterogeneous priors. |
| title | Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2505.04122 |