This chapter offers a brief survey of the theory of coalition formation introduced by Von Neumann and Morgenstern. The coalitional form of a game is defined and discussed. The idea of the core of a game is explained, together with its application to Walrasian equilibria. The Condorcet paradox is used in the game Odd-Man-Out to illustrate the myopia attributed to players by the core concept. This serves as an introduction to the idea of a Von Neumann and Morgenstern stable set. The Three-Cake Game is used to illustrate both the core, stable sets, and the Shapley value. The progress made in applying the Nash program in this area — for example, to the case of one seller and several buyers — is reviewed.
Keywords: Von Neumann and Morgenstern, coalitional form, transferable utility, Condorcet paradox, Odd-Man-Out, stable sets, Three-Cake Game, Shapley value, bargaining pit model, telephone bargaining model
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