Co-operative games theory (1940S)

A branch of game theory dealing with co-operative rather than simply competitive players.

Game theory attempts to study the interaction of individual decisions (given specific assumptions about decisions made under risk), the general environment and individual behavior patterns.

Co-operative games theory is used in the analysis of cartels and other forms of market collusion.

In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players (“coalitions”) due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats).

Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players’ actions and payoffs and analyzing Nash equilibria.

Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperative game theory also looks at how bargaining procedures will affect the distribution of payoffs within each coalition. As non-cooperative game theory is more general, cooperative games can be analyzed through the approach of non-cooperative game theory (the converse does not hold) provided that sufficient assumptions are made to encompass all the possible strategies available to players due to the possibility of external enforcement of cooperation. While it would thus be possible to have all games expressed under a non-cooperative framework, in many instances insufficient information is available to accurately model the formal procedures available to the players during the strategic bargaining process, or the resulting model would be of too high complexity to offer a practical tool in the real world. In such cases, cooperative game theory provides a simplified approach that allows the analysis of the game at large without having to make any assumption about bargaining powers.

Cooperative game theory assumes that groups of players, called coalitions, are the primary units of decision-making, and may enforce cooperative behavior. Consequently, cooperative games can be seen as a competition between coalitions of players, rather than between individual players. The basic assumption in cooperative game theory is that the grand coalition, that is the group consisting of all players, will form. One of the main research questions in cooperative game theory is how to allocate in some fair way the payoff of the grand coalition among the players. The answer to this question is related to a solution concept which, roughly speaking, is a vector that represents the allocation to each player. Different solution concepts based on different notions of fairness have been proposed in the cooperative game theory literature.