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A global Newton method to compute Nash equilibria

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  • Govindan, Srihari
  • Wilson, Robert

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  • Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    • Handle: RePEc:eee:jetheo:v:110:y:2003:i:1:p:65-86
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    References listed on IDEAS

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    1. Robert Wilson, 1972. "Computing Equilibria of Two-Person Games from the Extensive Form," Management Science, INFORMS, vol. 18(7), pages 448-460, March.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    4. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
    5. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    6. Yamamoto, Yoshitsugu, 1993. "A Path-Following Procedure to Find a Proper Equilibrium of Finite Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 249-259.
    7. Keenan, Donald, 1981. "Further remarks on the Global Newton method," Journal of Mathematical Economics, Elsevier, vol. 8(2), pages 159-165, July.
    8. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    10. Joseph T. Howson, Jr. & Robert W. Rosenthal, 1974. "Bayesian Equilibria of Finite Two-Person Games with Incomplete Information," Management Science, INFORMS, vol. 21(3), pages 313-315, November.
    11. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
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    Citations

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    Cited by:

    1. Dang, Chuangyin & Meng, Xiaoxuan & Talman, Dolf, 2015. "An Interior-Point Path-Following Method for Computing a Perfect Stationary Point of a Polynomial Mapping on a Polytope," Discussion Paper 2015-019, Tilburg University, Center for Economic Research.
    2. Sam Ganzfried & Austin Nowak & Joannier Pinales, 2018. "Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game," Papers 1804.04789, arXiv.org.
    3. Thompson, David R.M. & Leyton-Brown, Kevin, 2017. "Computational analysis of perfect-information position auctions," Games and Economic Behavior, Elsevier, vol. 102(C), pages 583-623.
    4. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    5. Sam Ganzfried, 2018. "Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations," Papers 1803.00607, arXiv.org, revised Jan 2019.
    6. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    7. Turocy, Theodore L., 2005. "A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence," Games and Economic Behavior, Elsevier, vol. 51(2), pages 243-263, May.
    8. Srihari Govindan & Robert Wilson, 2010. "A decomposition algorithm for N-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 97-117, January.
    9. Zheng-Hai Huang & Liqun Qi, 2017. "Formulating an n-person noncooperative game as a tensor complementarity problem," Computational Optimization and Applications, Springer, vol. 66(3), pages 557-576, April.
    10. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
    11. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.
    12. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    13. Govindand, Srihari & Wilson, Robert B., 2008. "Computing Equilibria of N-Player Games with Arbitrary Accuracy," Research Papers 1984, Stanford University, Graduate School of Business.
    14. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 1-7, January.
    15. repec:gam:jgames:v:9:y:2018:i:2:p:33-:d:151337 is not listed on IDEAS
    16. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, University Library of Munich, Germany, revised 16 Oct 2003.
    17. Jiang, Albert Xin & Leyton-Brown, Kevin, 2015. "Polynomial-time computation of exact correlated equilibrium in compact games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 347-359.
    18. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    19. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    20. Tadashi Yagi, 2014. "Knowledge Creation by Consumers and Optimal Strategies of Firms," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 5(3), pages 585-596, September.
    21. Anne Balthasar, 2010. "Equilibrium tracing in strategic-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 39-54, January.
    22. Yin Chen & Chuangyin Dang, 2016. "A reformulation-based smooth path-following method for computing Nash equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 231-246, October.

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