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

2026-02-04

AI Summary

This study investigates solution concepts—including the core, (pre-)nucleolus, kernel, and Mas-Colell bargaining set—in ex-ante cooperative games with uncertainty modeled via belief functions (Bel games). The authors employ Dempster–Shafer evidence theory to represent players’ prior beliefs over states and use Choquet integrals to capture their non-additive preferences. For the first time, they systematically develop multiple classical solution concepts within an ex-ante framework, revealing their geometric structures and mutual inclusion relations. Notably, in convex Bel games, they establish the coincidence of the core and the bargaining set, a result that necessitates a strengthened definition of the bargaining set. The work demonstrates the robustness of key properties from classical cooperative game theory under uncertainty and thereby extends the theoretical foundations of non-additive cooperative games.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Bel coalitional games
• ex-ante core
• solution concepts
• uncertainty
• Dempster-Shafer theory

Innovation

• Bel coalitional games
• ex-ante core
• Dempster-Shafer theory
• Choquet integral
• bargaining set