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Volumn , Issue , 2003, Pages 74-79

Using Computer Algebra To Find Nash Equilibria

Author keywords

Game theory; Gr bner bases; Polyhedral homotopy continuation; Polynomial systems

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SOFTWARE; GAME THEORY; POLYNOMIALS; PROBLEM SOLVING;

EID: 1542330056     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/860854.860879     Document Type: Conference Paper
Times cited : (22)

References (20)
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  • 2
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    • Universality of Nash equilibria. to appear. Preprint (arXiv:math.AG0301001)
    • R. S. Datta. Universality of Nash equilibria. Mathematics of Operations Research, to appear. Preprint (arXiv:math.AG0301001).
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  • 4
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    • T. Emiris and J. Canny. Efficient incremental algorithms for the sparse resultant and the mixed volume. Journal of Symbolic Computation, 20(2):117-149. 1995.
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    • Emiris, T.1    Canny, J.2
  • 9
    • 1542268076 scopus 로고    scopus 로고
    • PHoM - A polyhedral homotopy continuation method for polynomial systems
    • Tokyo Institute of Technology, Tokyo, January
    • T. Gunji, S. Kim, M. Kojima, A. Takeda, K. Fujisawa, and T. Mizutani. PHoM - a polyhedral homotopy continuation method for polynomial systems. Research Report B-386, Tokyo Institute of Technology, Tokyo, January 2003. http://www.is.titech.ac.jp/~kojima/PHoM/.
    • (2003) Research Report , vol.B-386
    • Gunji, T.1    Kim, S.2    Kojima, M.3    Takeda, A.4    Fujisawa, K.5    Mizutani, T.6
  • 10
    • 0000986569 scopus 로고
    • Oddness of the number of equilibrium points: A new proof
    • J. Harsanyi. Oddness of the number of equilibrium points: a new proof. International Journal of Game Theory, 2:235-250, 1973.
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    • Harsanyi, J.1
  • 11
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    • A polyhedral method for solving sparse polynomial systems
    • B. Huber and B. Sturmfels. A polyhedral method for solving sparse polynomial systems. Mathematics of Computation, 64:1541-1555, 1995.
    • (1995) Mathematics of Computation , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 13
    • 0031065971 scopus 로고    scopus 로고
    • The maximal number of regular totally mixed Nash equilibria
    • R. McKelvey and A. McLennan. The maximal number of regular totally mixed Nash equilibria. Journal of Economic Theory, 72:411-425, 1997.
    • (1997) Journal of Economic Theory , vol.72 , pp. 411-425
    • McKelvey, R.1    McLennan, A.2
  • 15
    • 0036171704 scopus 로고    scopus 로고
    • A new algorithm for discussing Groebner bases with parameters
    • A. Montes. A new algorithm for discussing Groebner bases with parameters. Journal of Symbolic Computation, 33(2): 183-208, 2002.
    • (2002) Journal of Symbolic Computation , vol.33 , Issue.2 , pp. 183-208
    • Montes, A.1
  • 18
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795: Phcpack: A general-purpose solver for polynomial systems by homotopy continuation
    • J. Verschelde. Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. ACM Transactions on Mathematical Software, 25(2):251-276, 1999.
    • (1999) Acm Transactions on Mathematical Software , vol.25 , Issue.2 , pp. 251-276
    • Verschelde, J.1
  • 19
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    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • J. Verscheide, P. Verlinden, and R. Cools. Homotopies exploiting Newton polytopes for solving sparse polynomial systems. SIAM Journal of Numerical Analysis, 31(3):915-930, 1994.
    • (1994) SIAM Journal of Numerical Analysis , vol.31 , Issue.3 , pp. 915-930
    • Verscheide, J.1    Verlinden, P.2    Cools, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.