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Game Theory in Economics

Chapter 6, Characteristic Function, Core, and Stable Set

by Lloyd S. Shapley, Martin Shubik

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The sixth chapter of a manuscript dealing with the applications of game theory to economic analysis, this study develops the notion of "characteristic function," a way of expressing very concisely the capabilities of each coalition in a cooperative game. Several special classes of games are then identified and discussed briefly: symmetric games, measure games, simple (voting) games, and "Edgeworth" and "Bohm-Bawerk" market games. Two important solution concepts are then introduced: the core and the stable set. Their heuristic interpretations are discussed and illustrated by simple examples. A final section introduces the general notion of a market game, and the closely related technical concept of balanced families of sets. A descriptive bibliography, containing more than 100 articles and books dealing with stable sets, is included as an appendix. (See also R-904/1, R-904/2, R-904/3.)

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