One can divide the study of game theory into two parts – the study of non-cooperative games, and the study of cooperative games. Strategic games model situations in which individual agents selfishly maximize their utility and there is no cooperation, while in cooperative (coalitional) games, the goal is to model situations where the players either benefit by working together or by sharing some sort of cost, but they are still selfish in that they will cooperate only if it benefits their self-interests.
It is worth noting that, “Cooperative Games simply refer to the enforcement level found in binding vs non-binding agreements” and “does not necessarily refer to a player’s ability to or desire to cooperate”. – Kyle Birchard.
Some others have gone through great lengths to provide us with comprehensive definitions of the differences between non-cooperative and cooperative games in Game Theory:
John Harsanyi provided a now commonly used definition of cooperative vs. non-cooperative games in his A General Theory of Rational Behavior in Game Situations, in which he stated: “A game is cooperative if commitments – agreements, promises, threats – are fully binding and enforceable. It is non-cooperative if commitments are not enforceable.”
John Nash distinguished between Cooperative and Non-cooperative Game Theory when he said, “This (cooperative game) theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game. Our (non-cooperative game) theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others.”
Parrachino, Zara & Patrone state on the difference between Non-cooperative and Cooperative Game Theory: “The main distinction between the two is that non-cooperative game theory models situations where players see only their own strategic objectives and thus binding agreements among the players are not possible, while cooperative game theory actually is based mainly on agreements to allocate cooperative gains (solution concepts). Therefore, while non-cooperative game theory models describe and take into account the strategic interaction among the players, cooperative game theory ignores the strategic stages leading to coalition building and focuses on the possible results of the cooperation.”
While, according to Olivier Chatain, “Non-cooperative game theory models the actions of agents, maximizing their utility in a defined procedure, relying on a detailed description of the moves and information available to each agent. Cooperative game theory abstracts from these details and focuses on how the value creation abilities of each coalition of agents can bear on the agents’ ability to capture value. Cooperative game theory can be thus called coalitional, while non-cooperative game theory is procedural. Note that ‘cooperative’ and ‘non-cooperative’ are technical terms and are not an assessment of the degree of cooperation among agents in the model: a cooperative game can as much model extreme competition as a non-cooperative game can model cooperation.” – Cooperative and Non-Cooperative Game Theory.
In his paper Non-cooperative Games, John Nash “drew the all-important distinction between non-cooperative and cooperative games, namely between games where players act on their own ‘without collaboration or communication with any of the others’, and ones where players have opportunities to share information, make deals, and join coalitions.” – Sylvia Nasar, The Essential John Nash.
As John Nash introduced us to the difference between cooperative and non-cooperative games, let us consider his words directly:
“The distinction between cooperative and non-cooperative games is unrelated to the mathematical description… rather it depends on the possibility or impossibility of coalitions, communication, and side-payments… [I] have developed a dynamic approach to the study of cooperative games based upon reduction to non-cooperative form. Thus, the problem analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation.” – Non-cooperative Games
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