Cooperative games with uncertainty: a survey

TL;DR

This survey reviews models of cooperative game theory that incorporate uncertainty, highlighting their differences, especially in terms of allocation and core concepts, from foundational work to recent contributions.

Contribution

It provides a comprehensive comparison of various models of uncertain cooperative games, including the authors' new Bel coalitional games model.

Findings

Different models handle uncertainty uniquely

All models propose a core concept for allocations

The survey clarifies the relationships among models

Abstract

The main stream of the literature in cooperative game theory considers games as being deterministic. In this survey, we review the main models incorporating uncertainty in cooperative games, starting from the seminal paper of Charnes and Granot (1976) and finishing with our own contribution, called Bel coalitional games. The different models are explained and compared, making a focus on the notion of allocation and core, since all the described models propose a notion of core.