Cooperative Game Theory
Overview
Cooperative game theory is a branch of game theory that focuses on predicting which coalitions will form, the joint actions that groups take, and the resulting collective payoffs. It is distinct from the theory of non-cooperative games in which the concept of a coalition is not recognized, and participants are not able to make enforceable agreements.
History
The origins of cooperative game theory can be traced back to the work of Hungarian mathematician John von Neumann and economist Oskar Morgenstern. Their book, "Theory of Games and Economic Behavior", published in 1944, laid the groundwork for the field.
Concepts and Definitions
Cooperative game theory is built upon several key concepts and definitions.
Coalitions
A coalition is a group of players who have decided to work together. In cooperative games, players are allowed to form coalitions to achieve a common goal.
Core
The core of a game is a set of outcomes that cannot be improved upon by a subset (coalition) of the players. If an outcome is in the core, it means that there is no coalition that would prefer to break away and play the game on their own.
Shapley Value
The Shapley value is a solution concept in cooperative game theory. It was named after Lloyd Shapley, who introduced it in 1953. The Shapley value provides a way to distribute the total payoff of a game to the players based on their marginal contribution to the total payoff.
Applications
Cooperative game theory has found applications in a variety of fields, including economics, political science, and computer science.
Economics
In economics, cooperative game theory is used to analyze situations where players can make binding agreements. Examples include the study of cooperative games in the context of oligopoly theory, bargaining theory, and coalition formation.
Political Science
In political science, cooperative game theory is used to study coalition formation, voting behavior, and power distribution among different players.
Computer Science
In computer science, cooperative game theory is used in the design of algorithms and protocols where users can form coalitions. Examples include the study of cooperative games in the context of network routing and task allocation in multi-agent systems.
Criticisms and Limitations
While cooperative game theory provides a powerful tool for analyzing situations where players can make binding agreements, it also has its limitations and has been subject to criticism. Some critics argue that the assumptions of cooperative game theory are not realistic in many situations. For example, the assumption that players can make binding agreements is not always valid, especially in situations where enforcement is difficult or impossible.