Stackelberg-Cournot-Nash equilibria under ambiguity and α-maxmin preferences

A Kantorovich-like optimal transport problem is formulated by seeking to minimize the Choquet integral of a given cost function with respect to the α-mixture of joint belief functions with given marginals, and their dual plausibility functions. This extension of the classical probabilistic problem allows to deal with misspecified marginal
distributions by relying on a parameter that acts like a pessimism index. 

We show that the particular subcase given by a marginal belief function and a marginal probability measure can be used to model a game under ambiguity, through the definition of the Stackelberg-Cournot-Nash equilibrium with Dempster-Shafer uncertainty and α-maxmin preferences. An algorithm is provided for approximating an equilibrium based on a suitable entropic formulation of the defined optimal transport problem. 

Finally, an application is found in a market with a finite set of types of investors and misspecified distributions. 

Investors’ choices result in a purchase portfolio on a finite set of assets which, in turn, depends on asset prices fixed by the market maker and the interactions among investors.

Short Bio: Silvia Lorenzini obtained her bachelor’s and master’s Degrees from the Department of Mathematics and Computer Science, University of Perugia, Italy. She will soon complete her doctoral studies in Quantitative Methods for Economics at the same University.