The core of games on ordered structures and graphs

TL;DR

This paper explores the properties of the core in cooperative games when the set of feasible coalitions is restricted, providing a unified framework for various existing results.

Contribution

It offers a comprehensive unification of different results concerning the core in cooperative games with restricted feasible coalitions.

Findings

Characterizes the core structure under various feasibility constraints

Provides a unified theoretical framework for existing results

Analyzes implications of coalition feasibility on core properties

Abstract

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results.