Cooperative Game Theory

Cooperative game theory studies situations where players can form binding agreements and coalitions, in contrast to non-cooperative game theory where individual strategy choice is paramount. The field was initiated by John von Neumann and Oskar Morgenstern in their 1944 treatise, who introduced the characteristic function as a way to represent what each coalition of players can guarantee itself regardless of what outsiders do.

The central problem of cooperative game theory is not strategic reasoning but distributive justice: given that a coalition can achieve some collective payoff, how should that payoff be divided among members? The von Neumann-Morgenstern stable set was the first solution concept, but it was eventually supplemented and displaced by the Nash bargaining solution and, more durably, by the Shapley value — which assigns to each player their marginal contribution averaged over all possible coalition-formation orders. The field remains essential to mechanism design, political coalition theory, and cost allocation problems.