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The Algebraic Geometry of Games and the Tracing Procedure

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Abstract

This paper has two purposes. The immediate purpose is to point out some difficulties with the tracing procedure of Harsanyi and Selten, and show how they can be dealt with. The other purpose is to describe the theory of semi-algebraic sets and a few of its applications in game theory.

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References

  • T. Bewley and E. Kohlberg [ 1976 ], The Asymptotic Solution of a Recursion Equation Occurring in Stochastic Games,“ Mathematics of Operations Research, 1, 321–336.

    Article  Google Scholar 

  • L. Blume and W. R. Zame [ 1989 ], The Algebraic Geometry of Perfect and Sequential Equilibrium,“ Working Paper, Center for Analytic Economics, Cornell University.

    Google Scholar 

  • J. Bochnak, M. Coste, M-F. Roy [ 1987 ], Geometrie Algebrique Reele, Springer-Verlag, Berlin.

    Google Scholar 

  • H. Dells and M. Knebusch [ 1981a ], “Semi-Algebraic Topology over a Real Closed Field I,” Mathematische Zeitschrift, 177, 107–129.

    Article  Google Scholar 

  • H. Dells and M. Knebusch 11981b1, “Semi-Algebraic Topology over a Real Closed Field II,” Mathematische Zeitschrift, 178, 175–213.

    Google Scholar 

  • R. Hardt [ 1980 ], “Semi-Algebraic Local Triviality in Semi-Algebraic Mappings,” American Journal of Mathematics, 102, 291–302.

    Article  Google Scholar 

  • J. C. Harsanyi [1975], “The Tracing Procedure: A Bayesian Approach to Defining a Solution for n-Person Noncooperative Games,“ International Journal of Game Theory,4 61–94.

    Google Scholar 

  • J. C. Harsanyi and R. Selten [19881, A General Theory of Equilibrium Selection in Games,MIT Press, Cambridge.

    Google Scholar 

  • W. Hildenbrand [ 1974 ], Core and Equilbria of a Large Economy, Princeton University Press, Princeton, N.J.

    Google Scholar 

  • H. Hironaka [ 1975 ], “Triangulations of Algebraic Sets,” in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence.

    Google Scholar 

  • E. Kohlberg and J. F. Mertens [ 1986 ], On the Strategic Stability of Equilibria,“ Econometrica, 54, 1003–1037

    Article  Google Scholar 

  • D. M. Kreps and R. Wilson [ 1982 ], “Sequential Equilibria,” Econometrica, 50, 863–894.

    Article  Google Scholar 

  • S. Lojasiewicz [ 1964 ], “Triangulations of Semi-Analytic Sets,” Annali Scuola Normale Superiore di Pisa, 18, 449–474.

    Google Scholar 

  • S. Lojasiewicz [ 1965 ], “Ensembles Semi-Analytiques,” Publication I.H.E.5.

    Google Scholar 

  • J. Milnor [ 1968 ], Singular Points of Complex Hypersurfaces, Princeton University Press, Princeton.

    Google Scholar 

  • A. Seidenberg [ 1954 ], “A New Decision Method for Elementary Algebra,” Annals of Mathematics, 60, 365–374.

    Article  Google Scholar 

  • R. Selten [19751, “Re-examination of the Perfectness Concept for

    Google Scholar 

  • Equilibrium Points in Extensive Games,“ International Journal of Game Theory,4, 25–55.

    Google Scholar 

  • L. Simon [ 1987 ], “Basic Timing Games,” Working Paper, University of California at Berkeley.

    Google Scholar 

  • A. Tarski [19311, “Sur les Ensembles Definissables de Nombres Reels,” Fundamenta Mathematica, 17, 210–239.

    Google Scholar 

  • E. van Damme [19871, Stability and Perfection of Nash Equilibria,Springer-Verlag, New York.

    Google Scholar 

  • L. van den Dries [ 1981, “A Generalization of the Tarski-Seidenberg Theorem, and Some Non-definability Results,” Bulletin of the American Mathematical Society, 15, 189–193.

    Article  Google Scholar 

  • H. Whitney [ 1957 ], “Elementary Structure of Real Algebraic Varieties,” Annals of Mathematics, 66, 545–556.

    Article  Google Scholar 

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© 1991 Springer-Verlag Berlin Heidelberg

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Schanuel, S.H., Simon, L.K., Zame, W.R. (1991). The Algebraic Geometry of Games and the Tracing Procedure. In: Selten, R. (eds) Game Equilibrium Models II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07365-0_3

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  • DOI: https://doi.org/10.1007/978-3-662-07365-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08109-5

  • Online ISBN: 978-3-662-07365-0

  • eBook Packages: Springer Book Archive

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