In this paper we offer the reader an opportunity to inspect, at close hand, the substance and methodology of a special corner of descriptive game theory. The “simple games” that populate this area are finite, combinatorial structures that are not only amusing to mathematicians but can serve as abstract representations of voting systems or other group-decision procedures. As such, they have found applications in political science and organization theory, as well as in certain branches of pure mathematics.
KeywordsSimple Game Winning Coalition Individual Player Minimal Winning Coalition Substitution Property
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- *.Theory of Games and Economic Behavior, Princeton University Press, 1944, 1947, 1953.Google Scholar
- **.Some recent examples: J. R. Isbell, “Homogeneous Games III” and L. S. Shapley, “Compound Simple Games,” in Advances in Game Theory: Annals of Mathematics Study-No, 52, Princeton University Press, 1964; W. H. Riker and L. S. Shapley, “Weighted voting: a mathematical analysis for instrumental judgments.” in Nomos X: Representation (Yearbook of the American Society for Political and Legal Philosophy), Atherton Press, New York, 1967. for a short expository article with a complete bibliography to date, see this author’s Simple games: an outline of the descriptive theory, RAND Corporation Paper P-2277, April 1961. (Also published without bibliography in Behavioral Science 7 (1962), pp. 59–66.)Google Scholar