Properties of the core and other solution concepts of Bel coalitional games in the ex-ante scenario

TL;DR

This paper explores the properties of the core and other solution concepts in Bel coalitional games under uncertainty, focusing on the ex-ante scenario where contracts are evaluated before the true state of the world is known.

Contribution

It extends classical coalitional game solution concepts to uncertain environments using Dempster-Shafer theory and Choquet integrals, analyzing their geometrical and relational properties.

Findings

Ex-ante core and bargaining set inclusion relations mirror classical cases.

Coincidence of ex-ante core and bargaining set occurs in convex games with strengthened definitions.

The geometrical structure of the ex-ante core is characterized when agents share the same probability-based knowledge.

Abstract

We study the properties of the core and other solution concepts of Bel coalitional games, that generalize classical coalitional games by introducing uncertainty in the framework. In this uncertain environment, we work with contracts, that specify how agents divide the values of the coalitions in the different states of the world. Every agent can have different a priori knowledge on the true state of the world, which is modeled through the Dempster-Shafer theory, while agents' preferences between contracts are modeled by the Choquet integral. We focus on the "ex-ante" scenario, when the contract is evaluated before uncertainty is resolved. We investigate the geometrical structure of the ex-ante core when agents have the same a priori knowledge which is a probability distribution. Finally, we define the (pre)nucleolus, the kernel and the bargaining set (a la Mas-Colell) in the ex-ante situation and we study their properties. It is found that the inclusion relations among these solution concepts are the same as in the classical case. Coincidence of the ex-ante core and the ex-ante bargaining set holds for convex Bel coalitional games, at the price of strengthening the definition of bargaining sets.