Optimal transport in Dempster–Shafer theory and its applications in game theory

Classical optimal transport assumes fully specified probability distributions. This talk relaxes that requirement by representing partially known marginals with belief functions. It examines joint belief functions with fixed marginals and minimizes a Choquet integral of transport cost. Preferences use an α-maxmin criterion, with α between zero and one measuring pessimism. When the cost is a ground metric, the construction gives a Choquet–Wasserstein pseudo-distance for comparing belief functions on a common space.

The same framework describes games under ambiguity through a Stackelberg–Cournot–Nash equilibrium with Dempster–Shafer uncertainty and α-maxmin preferences. An application considers a continuum of investors whose type distribution is only partly known: investors choose portfolios of assets while a market maker sets prices.