Abstract
This chapter explains the distinction between cooperative multi-person games in which binding agreements and coalition formation among the players are permitted, and non-cooperative games in which they are not. It discusses non-cooperative theory, which is based on equilibrium points, and the solutions are shown to be weak in many cases. The chapter focuses on cooperative theory, which makes use of a mathematical formalization, known as the characteristic function, of the value of coalitions to their members. Harold Pinter's play, the Caretaker, is used in the chapter to illustrate the shifting pattern of coalitions in a three-person game with an empty core; that is, one in which a potential coalition exists with the will and the power to replace any existing coalition. Thw chapter also discusses the Shapley value, a measure of the player's a priori power in a game and presents interesting and unexpected results to result from its application to the United Nations Security Council and other real decision making bodies. Societies have a tendency to evolve toward stable states in which all, none, or some fixed proportion of individuals act cooperatively toward each other in two-person interactions with specified strategic structures.
Published Version
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