Value Solutions in Cooperative Games

This book introduces new concepts for cooperative game theory, and particularly solutions that determine the distribution of a coalitional surplus among the members of the coalition. It also addresses several generalizations of cooperative game theory. Drawing on methods of welfare economics, new value solutions are derived for Non-Transferable Utility games with and without differences of bargaining power among the members of the coalition. Cooperation in intertemporal games is examined, and conditions that permit the reduction of these games to games in coalition function form are outlined. Biform games and games that combine non-cooperative search and matching of coalition members with cooperative solutions (i.e., efficient contracts) within the coalition are considered.

Contents:

• Value Solutions for Superadditive Transferable Utility Games in Coalition Function Form
• Zeuthen–Nash Bargaining
• Nontransferable Utility Games and Games in Partition Function Form
• A Shapley Value Algorithm for Games in Partition Function Form
• Extension of the Nucleolus to Nontransferable Utility Games in Partition Function Form
• A Core Imputation with Variable Bargaining Power
• Bargaining Power Biform Games
• Intertemporal Cooperative Games: A Sketch of a Theory
• A Theory of Enterprise

Readership: Graduate students and researchers in the field of game theory.
Key Features:

• Proposes a value solution for games of two or more players that: (i) is the Nash bargaining solution in a special case, (ii) allows for unsymmetrical bargaining power, (iii) allows for group-to-group bargaining, and (iv) is always a point in the core of the game if the game is not null
• Uses methods from mathematical welfare economics to bridge the gap from non-transferable utility to transferable utility
• Relying on Biform Games (Brandenburger and Stuart), constructs a model of cooperative value creation in coalitions formed by non-cooperative search and matching