Cooperative games with uncertainty: a survey

2026-02-27

AI Summary

This study addresses the limitation of classical cooperative game theory, which typically assumes a deterministic environment and thus struggles to capture real-world uncertainty. The paper provides a systematic review of cooperative game models incorporating uncertainty since the seminal work of Charnes and Granot (1976), integrating modeling tools from fuzzy set theory, probability theory, and belief functions. It establishes, for the first time, a unified framework to comparatively analyze solution concepts—particularly allocation rules and the core—across these diverse models. Notably, the authors introduce the “Bel coalition game,” a novel model grounded in belief functions, which clarifies the interrelationships and distinctions among existing approaches to uncertainty in cooperative games. This framework offers a coherent analytical foundation and clear pathways for future theoretical development and practical applications.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• cooperative games
• uncertainty
• core
• allocation
• Bel coalitional games

Innovation

• cooperative games
• uncertainty
• Bel coalitional games
• core
• allocation