By Dieudonne J.
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Extra info for A Generalization of Rolle's Theorem with Application to Entire Functions
The case is similar with regard to the introduction of the “dummy player” in order to diminish the complexity of the four-person game. The latter is considered to be essentially like a threeperson game. Falling back upon a ﬁctitious player permits them this time to apprehend all n-person general games as (n+1)-person zero-sum games. But the analogy between these two operations remains imperfect and the introduction of the ﬁctitious player raises additional problems. It cannot be guaranteed, for example, that the compensation of gains and losses for which the ﬁctitious player is ﬁctitiously responsible will have no inﬂuence over the course of the game.
1950), Statistical Decision Functions. New York: John Wiley and Sons. Weintraub, E. , ed. (1992), Toward a History of Game Theory. History of Political Economy, supplement to vol. 24, Durham and London: Duke University Press. Zermelo, E. (1913), “Uber eine Anwendung der Mengenlehre auf die theorie des Schachspiels,” Proceedings, Fifth International Conference of Mathematicians, 2, 501–4. , Readings in Games and Information. Malden, MA: Blackwell, 2001. © 1995 Éditions Dalloz English edition: editorial matter and selection © 2002 Christian Schmidt; individual chapters © the contributors 2 Rupture versus continuity in game theory Nash versus Von Neumann and Morgenstern Christian Schmidt Introduction The relationship between game theory and economic theory is neither simple nor one-sided.
2 This analogy depends on an interpretation of the axiomatization of utility developed by Savage. Indeed, according to Savage, the question is to ﬁnd a system of axioms compatible with the formulation of utility proposed by D. Bernouilli (Savage 1954: 58–9). The axioms presented in TGEB satisfy this condition. However, even as Peano’s axiomatic is compatible with other mathematical objects than the set of natural numbers, the axiomatic of utility in TGEB is also found to be satisﬁed by functions of utility other than that oﬀered by Bernouilli.
A Generalization of Rolle's Theorem with Application to Entire Functions by Dieudonne J.