Stochastic cooperative games of risk averse players and application to multiple newsvendors problem

TL;DR

This paper introduces a new solution concept called SSD-core for stochastic cooperative games with risk-averse players, linking it to cores of deterministic games and applying it to the multiple newsvendors problem.

Contribution

It proposes the SSD-core as a novel solution concept for risk-averse stochastic cooperative games and explores its properties and applications.

Findings

SSD-core connects to cores of deterministic games under uniform distribution.

Balancedness and convexity imply non-emptiness of SSD-core.

Application to multiple newsvendors problem characterizes risk-averse behavior.

Abstract

This paper studies the stochastic setting in cooperative games and suggests a solution concept based on second order stochastic dominance (SSD), which is often applied to robustly model risk averse behaviour of players in different economic and game theoretic models as it enables to model not specified levels of risk aversion among players. The main result of the paper connects this solution concept, \emph{SSD-core}, in case of uniform distribution of the game to cores of two deterministic cooperative games. Interestingly, balancedness of both of these games and convexity of one of these implies non-emptiness of the SSD-core. The opposite implication does not, in general, hold and leads to questions about intersections of cores of two games and their relations. Finally, we present an application of the SSD-core to the multiple newsvendors problem, where we provide a characterization of risk averse behaviour of players with an interpretation in terms of the model.