Risk Sharing Among Many: Implementing a Subgame Perfect and Optimal Equilibrium (2505.04122v2)

Abstract: Can a welfare-maximising risk-sharing rule be implemented in a large, decentralised community? We revisit the price and choice (P&C) mechanism of Echenique and N\'u~nez (2025), in which players post price schedules sequentially, and the final player selects an allocation. While P&C implements every Pareto-optimal allocation when the choice set is finite, realistic risk-sharing problems involve an infinite continuum of feasible allocations. We extend P&C to such infinite menus, modelling each allocation as a probability distribution that redistributes an aggregate loss $X=\sum_i X_i$. Every feasible allocation is comonotone, yet comonotonicity alone is not efficient when agents maximise monetary utility. We prove that our extended mechanism still implements the allocation that maximises aggregate utility, even when players entertain heterogeneous, uniformly tight credal sets over the distribution of $X$. Finally, we pair $P&C$ with a simple auction introduced by Echenique and N\'u~nez (2025) that chooses the first mover, equalising surplus among participants. The result is a decentralised, enforcement-free procedure that achieves both optimal and fair risk sharing under distributional uncertainty.