IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/65506.html
   My bibliography  Save this paper

Unit vector games

Author

Listed:
  • von Stengel, Bernhard
  • Savani, Rahul

Abstract

McLennan and Tourky (2010) showed that “imitation games” provide a new view of the computation of Nash equilibria of bimatrix games with the Lemke–Howson algorithm. In an imitation game, the payoff matrix of one of the players is the identity matrix. We study the more general “unit vector games”, which are already known, where the payoff matrix of one player is composed of unit vectors. Our main application is a simplification of the construction by Savani and von Stengel (2006) of bimatrix games where two basic equilibrium-finding algorithms take exponentially many steps: the Lemke–Howson algorithm, and support enumeration.

Suggested Citation

  • von Stengel, Bernhard & Savani, Rahul, 2016. "Unit vector games," LSE Research Online Documents on Economics 65506, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:65506
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/65506/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    3. McLennan, Andrew & Tourky, Rabee, 2010. "Imitation games and computation," Games and Economic Behavior, Elsevier, vol. 70(1), pages 4-11, September.
    4. Walter D. Morris, 1994. "Lemke Paths on Simple Polytopes," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 780-789, November.
    5. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    6. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    7. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    8. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    9. McLennan, Andrew & Park, In-Uck, 1999. "Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(1), pages 111-130, January.
    10. Rahul Savani & Bernhard Stengel, 2006. "Hard-to-Solve Bimatrix Games," Econometrica, Econometric Society, vol. 74(2), pages 397-429, March.
    11. Todd R. Kaplan & John Dickhaut, "undated". "A Program for Finding Nash Equilibria," Working papers _004, University of Minnesota, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2020. "Tournament-stable equilibria," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 41-51.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    2. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    3. Rahul Savani & Bernhard Stengel, 2015. "Game Theory Explorer: software for the applied game theorist," Computational Management Science, Springer, vol. 12(1), pages 5-33, January.
    4. Bharat Adsul & Jugal Garg & Ruta Mehta & Milind Sohoni & Bernhard von Stengel, 2021. "Fast Algorithms for Rank-1 Bimatrix Games," Operations Research, INFORMS, vol. 69(2), pages 613-631, March.
    5. Bernhard von Stengel & Antoon van den Elzen & Dolf Talman, 2002. "Computing Normal Form Perfect Equilibria for Extensive Two-Person Games," Econometrica, Econometric Society, vol. 70(2), pages 693-715, March.
    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. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    8. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    9. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    10. McLennan, Andrew & Tourky, Rabee, 2010. "Imitation games and computation," Games and Economic Behavior, Elsevier, vol. 70(1), pages 4-11, September.
    11. Jugal Garg & Ruta Mehta & Vijay V. Vaziranic, 2018. "Substitution with Satiation: A New Class of Utility Functions and a Complementary Pivot Algorithm," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 996-1024, August.
    12. F. Forges & B. von Stengel, 2002. "Computionally Efficient Coordination in Games Trees," THEMA Working Papers 2002-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    13. McLennan, Andrew & Tourky, Rabee, 2008. "Games in oriented matroids," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 807-821, July.
    14. Yin Chen & Chuangyin Dang, 2019. "A Reformulation-Based Simplicial Homotopy Method for Approximating Perfect Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 877-891, October.
    15. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Nov 2023.
    16. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Other publications TiSEM b8e0c74e-2219-4ab0-99a2-0, Tilburg University, School of Economics and Management.
    17. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    18. Pei, Ting & Takahashi, Satoru, 2019. "Rationalizable strategies in random games," Games and Economic Behavior, Elsevier, vol. 118(C), pages 110-125.
    19. R. B. Bapat & S. K. Neogy, 2016. "On a quadratic programming problem involving distances in trees," Annals of Operations Research, Springer, vol. 243(1), pages 365-373, August.
    20. P. Herings & Ronald Peeters, 2005. "A Globally Convergent Algorithm to Compute All Nash Equilibria for n-Person Games," Annals of Operations Research, Springer, vol. 137(1), pages 349-368, July.

    More about this item

    Keywords

    bimatrix game; Nash equilibrium computation; imitation game; Lemke–Howson algorithm; unit vector game;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:65506. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.