Christopher Blier-Wong
University of Toronto
Room: M3 3127
Risk sharing as a cooperative game
We study risk sharing among agents who evaluate losses through distortion risk measures. Efficient allocations are characterized by inf-convolution, and we implement them through deterministic monetary transfers that leave every agent at least as well off as acting alone. Cash additivity endows the set of individually rational transfers with a simplex geometry, reducing the implementation problem to splitting the aggregate welfare gain across agents.
We consider a hierarchy of desiderata for transfers, ranging from individual rationality to core stability, and characterize where an Arrow-Debreu pricing rule, the Shapley value, and the nucleolus each stand relative to these criteria. We then ask whether these rules are entry-monotone, that is, whether incumbents' welfare gains persist as the coalition grows. None of the canonical rules qualify in general, with pricing-based and cooperative rules failing through distinct mechanisms. We characterize entry-monotone implementations via population-monotonic allocation schemes and fully characterize the conditions under which they exist.