메뉴 건너뛰기




Volumn 73, Issue 1, 2005, Pages 141-174

The expected number of Nash equilibria of a normal form game

Author keywords

Algebraic geometry; Computational complexity; Nash equilibrium; Number of equilibria; Random games; Rotational invariance

Indexed keywords


EID: 27744581012     PISSN: 00129682     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1468-0262.2005.00567.x     Document Type: Article
Times cited : (51)

References (42)
  • 2
    • 27744557312 scopus 로고    scopus 로고
    • The asymptotic expected number of Nash equilibria of two player normal form games
    • forthcoming
    • BERG, J., AND A. MCLENNAN (2002): "The Asymptotic Expected Number of Nash Equilibria of Two Player Normal Form Games," Games and Economic Behavior, forthcoming.
    • (2002) Games and Economic Behavior
    • Berg, J.1    Mclennan, A.2
  • 3
    • 0003377844 scopus 로고
    • Rationalizable strategic behavior
    • BERNHEIM, B. D. (1984): "Rationalizable Strategic Behavior," Econometrica, 52, 1007-1028.
    • (1984) Econometrica , vol.52 , pp. 1007-1028
    • Bernheim, B.D.1
  • 6
    • 0010777778 scopus 로고
    • Probability of a pure equilibrium point in n-person games
    • DRESHER, M. (1970): "Probability of a Pure Equilibrium Point in n-Person Games," Journal of Combinatorial Theory, 8, 134-145.
    • (1970) Journal of Combinatorial Theory , vol.8 , pp. 134-145
    • Dresher, M.1
  • 8
    • 0000348667 scopus 로고
    • Efficient incremental algorithms for the sparse resultant and the mixed volume
    • EMIRIS, I. Z., AND J. F. CANNY (1995): "Efficient Incremental Algorithms for the Sparse Resultant and the Mixed Volume," Journal of Symbolic Computation, 20, 117-149.
    • (1995) Journal of Symbolic Computation , vol.20 , pp. 117-149
    • Emiris, I.Z.1    Canny, J.F.2
  • 12
    • 0039637282 scopus 로고
    • Mathematical programming and convex geometry
    • ed. by P. M. Gruber and J. M. Wills. New York: North-Holland
    • GRITZMAN, P., AND V. KLEE (1993): "Mathematical Programming and Convex Geometry," in Handbook of Convex Geometry, Vol. A, ed. by P. M. Gruber and J. M. Wills. New York: North-Holland, 627-674.
    • (1993) Handbook of Convex Geometry , vol.A , pp. 627-674
    • Gritzman, P.1    Klee, V.2
  • 14
    • 0000986569 scopus 로고
    • Oddness of the number of equilibrium points: A new proof
    • HARSANYI, J. C. (1973): "Oddness of the Number of Equilibrium Points: A New Proof," International Journal of Game Theory, 2, 235-250.
    • (1973) International Journal of Game Theory , vol.2 , pp. 235-250
    • Harsanyi, J.C.1
  • 16
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial systems
    • HUBER, B., AND B. STURMFELS (1995): "A Polyhedral Method for Solving Sparse Polynomial Systems," Mathematics of Computation, 64, 1541-1555.
    • (1995) Mathematics of Computation , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 17
    • 42549171482 scopus 로고
    • On the average number of real roots of a random algebraic equation
    • KAC, M. (1943): "On the Average Number of Real Roots of a Random Algebraic Equation," Bulletin of the American Mathematical Society, 49, 314-320 and 938.
    • (1943) Bulletin of the American Mathematical Society , vol.49 , pp. 314-320
    • Kac, M.1
  • 18
    • 0031256798 scopus 로고
    • On the maximal number of Nash equilibria in a bimatrix game
    • KEIDING, H. (1995): "On the Maximal Number of Nash Equilibria in a Bimatrix Game," Games and Economic Behavior, 21, 148-160.
    • (1995) Games and Economic Behavior , vol.21 , pp. 148-160
    • Keiding, H.1
  • 19
    • 0034311074 scopus 로고    scopus 로고
    • Correlated equilibria of games with many players
    • KEIDING, H., AND B. PELEG (2000): "Correlated Equilibria of Games with Many Players," International Journal of Game Theory, 29, 375-389.
    • (2000) International Journal of Game Theory , vol.29 , pp. 375-389
    • Keiding, H.1    Peleg, B.2
  • 20
    • 0000292804 scopus 로고
    • On the strategic stability of equilibria
    • KOHLBERG, E., AND J.-F. MERTENS (1986): "On the Strategic Stability of Equilibria," Econometrica, 54, 1003-1038.
    • (1986) Econometrica , vol.54 , pp. 1003-1038
    • Kohlberg, E.1    Mertens, J.-F.2
  • 21
    • 0009877344 scopus 로고
    • On the distribution of roots of random polynomials
    • ed. by M. Hirsch, J. Marsden, and M. Snub. New York: Springer-Verlag
    • KOSTLAN, E. (1993): "On the Distribution of Roots of Random Polynomials," in From Topology to Computation; Proceedings of the Smalefest, ed. by M. Hirsch, J. Marsden, and M. Snub. New York: Springer-Verlag, 419-431.
    • (1993) From Topology to Computation; Proceedings of the Smalefest , pp. 419-431
    • Kostlan, E.1
  • 22
    • 27844464014 scopus 로고    scopus 로고
    • On the expected number of real roots of a system of random polynomial equations
    • ed. by F. Cucker and M. Rojas. River Edge, NJ: World Scientific
    • _ (2002): "On the Expected Number of Real Roots of a System of Random Polynomial Equations," in Foundations of Computational Mathematics: Proceedings of the Smalefest 2000, ed. by F. Cucker and M. Rojas. River Edge, NJ: World Scientific, 149-188.
    • (2002) Foundations of Computational Mathematics: Proceedings of the Smalefest 2000 , pp. 149-188
  • 24
    • 0031065971 scopus 로고    scopus 로고
    • The maximal number of regular totally mixed Nash equilibria
    • MCKELVEY, R. D., AND A. MCLENNAN (1997): "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, 72, 411-425.
    • (1997) Journal of Economic Theory , vol.72 , pp. 411-425
    • Mckelvey, R.D.1    Mclennan, A.2
  • 25
    • 0031065973 scopus 로고    scopus 로고
    • The maximal generic number of pure Nash equilibria
    • MCLENNAN, A. (1997): "The Maximal Generic Number of Pure Nash Equilibria," Journal of Economic Theory, 72, 408-410.
    • (1997) Journal of Economic Theory , vol.72 , pp. 408-410
    • Mclennan, A.1
  • 26
    • 0009847775 scopus 로고    scopus 로고
    • The maximal number of real roots of a multihomogeneous system of polynomial equations
    • _ (1999): "The Maximal Number of Real Roots of a Multihomogeneous System of Polynomial Equations," Beiträge zur Algebra und Geometrie, 40, 343-350.
    • (1999) Beiträge zur Algebra und Geometrie , vol.40 , pp. 343-350
  • 27
    • 0036324756 scopus 로고    scopus 로고
    • The expected number of real roots of a multihomogeneous system of polynomial equations
    • _ (2002): "The Expected Number of Real Roots of a Multihomogeneous System of Polynomial Equations," American Journal of Mathematics, 124, 49-73.
    • (2002) American Journal of Mathematics , vol.124 , pp. 49-73
  • 28
    • 27744510760 scopus 로고    scopus 로고
    • Supplement to the expected number of Nash equilibria of a normal form game'
    • _ (2004): "Supplement to The Expected Number of Nash Equilibria of a Normal Form Game'," Econometrica Supplementary Material, http://www.econometricsociety.org/ecta/supmat/1712illustration.pdf.
    • (2004) Econometrica Supplementary Material
  • 29
    • 0042204039 scopus 로고    scopus 로고
    • Generic 4×4 games have at most 15 Nash equilibria
    • MCLENNAN, A., AND I.-U. PARK (1999): "Generic 4×4 Games Have at Most 15 Nash Equilibria," Games and Economic Behavior, 26, 111-130.
    • (1999) Games and Economic Behavior , vol.26 , pp. 111-130
    • Mclennan, A.1    Park, I.-U.2
  • 30
    • 0003986162 scopus 로고
    • Annals of Mathematics Studies. Princeton: Princeton University Press
    • MILNOR, J. W., AND J. D. STASHEFF (1974): Characteristic Classes, Annals of Mathematics Studies 76. Princeton: Princeton University Press.
    • (1974) Characteristic Classes , vol.76
    • Milnor, J.W.1    Stasheff, J.D.2
  • 31
    • 0000319051 scopus 로고
    • Rationalizable strategic behavior and the problem of perfection
    • PEARCE, D. G. (1984): "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, 52, 1029-1050.
    • (1984) Econometrica , vol.52 , pp. 1029-1050
    • Pearce, D.G.1
  • 32
    • 0010781233 scopus 로고
    • Limiting distributions of the number of pure strategy Nash equilibria
    • POWERS, I. (1990): "Limiting Distributions of the Number of Pure Strategy Nash Equilibria," International Journal of Game Theory, 19, 277-286.
    • (1990) International Journal of Game Theory , vol.19 , pp. 277-286
    • Powers, I.1
  • 33
    • 0040747444 scopus 로고    scopus 로고
    • A theorem on the number of Nash equilibria in a bimatrix game
    • QUINT, T., AND M. SHUBIK (1997): "A Theorem on the Number of Nash Equilibria in a Bimatrix Game," International Journal of Game Theory, 26, 353-360.
    • (1997) International Journal of Game Theory , vol.26 , pp. 353-360
    • Quint, T.1    Shubik, M.2
  • 34
    • 0009844162 scopus 로고    scopus 로고
    • On the average number of real roots of certain random sparse polynomial systems
    • ed. by J. Renegar, M. Shub, and S. Smale. Providence, RI: American Mathematical Society
    • ROJAS, J. M. (1996): "On the Average Number of Real Roots of Certain Random Sparse Polynomial Systems," in Lectures on Applied Mathematics Series, ed. by J. Renegar, M. Shub, and S. Smale. Providence, RI: American Mathematical Society, 689-699.
    • (1996) Lectures on Applied Mathematics Series , pp. 689-699
    • Rojas, J.M.1
  • 37
    • 0000537756 scopus 로고
    • Complexity of Bezout's theorem II: Volumes and probabilities
    • ed. by F. Eyssette and A. Galligo. Boston: Birkhauser
    • SHUB, M., AND S. SMALE (1993): "Complexity of Bezout's Theorem II: Volumes and Probabilities," in Computational Algebraic Geometry, Progress in Mathematics, Vol. 109, ed. by F. Eyssette and A. Galligo. Boston: Birkhauser, 267-285.
    • (1993) Computational Algebraic Geometry, Progress in Mathematics , vol.109 , pp. 267-285
    • Shub, M.1    Smale, S.2
  • 38
    • 0010847432 scopus 로고
    • A note on the probability of k pure Nash equilibria in matrix games
    • STANFORD, W. (1995): "A Note on the Probability of k Pure Nash Equilibria in Matrix Games," Games and Economic Behavior, 9, 238-246.
    • (1995) Games and Economic Behavior , vol.9 , pp. 238-246
    • Stanford, W.1
  • 40
    • 0028449799 scopus 로고
    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • VERSCHELDE, J., P. VERLINDEN, AND R. COOLS (1994): "Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems," SIAM Journal of Numerical Analysis, 31, 915-930.
    • (1994) SIAM Journal of Numerical Analysis , vol.31 , pp. 915-930
    • Verschelde, J.1    Verlinden, P.2    Cools, R.3
  • 41
    • 0033463683 scopus 로고    scopus 로고
    • New maximal numbers of equilibria in bimatrix games
    • VON STENGEL, B. (1999): "New Maximal Numbers of Equilibria in Bimatrix Games," Discrete and Computational Geometry, 21, 557-568.
    • (1999) Discrete and Computational Geometry , vol.21 , pp. 557-568
    • Von Stengel, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.