Advanced Search
MyIDEAS: Login to save this paper or follow this series

Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games


Author Info

  • Herings, P.J.J.
  • Elzen, A.H. van den

    (Tilburg University, Center for Economic Research)


Harsanyi and Selten (1988) have proposed a theory of equilibrium selection that selects a unique Nash equilibrium for any non-cooperative N-person game. The heart of their theory is given by the tracing procedure, a mathematical construction that adjusts arbitrary prior beliefs into equilibrium beliefs. The tracing procedure plays an important role in the definition of risk-dominance for Nash equilibria. Although the term "procedure" suggests a numerical approach, the tracing procedure itself is a non-constructive method. In this paper we propose a homotopy algorithm that generates a path of strategies. By employing lexicographic pivoting techniques it can be shown that for the entire class of non-cooperative N-person games the path converges to an approximate Nash equilibrium, even when the starting point or the game is degenerate. The outcome of the algorithm is shown to be arbitrarily close to the beliefs proposed by the tracing procedure. Therefore, the algorithm does not compute just any Nash equilibrium, but one with a sound gametheoretic underpinning. Like other homotopy algorithms, it is easily implemented on a computer. To show our results we apply methods from the theory of simplicial algorithms and algebraic geometry.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (Richard Broekman)
Download Restriction: no

Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1998-04.

as in new window
Date of creation: 1998
Date of revision:
Handle: RePEc:dgr:kubcen:199804

Contact details of provider:
Web page:

Related research

Keywords: Computation of equilibria; Non-cooperative game theory; Tracing procedure;

Other versions of this item:

Find related papers by JEL classification:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Doup, T.M. & Talman, A.J.J., 1986. "A continuous deformation algorithm on the product space of unit simplices," Research Memorandum 219, Tilburg University, Faculty of Economics and Business Administration.
  2. Elzen, A.H. van den & Talman, A.J.J., 1988. "A procedure for finding Nash equilibria in bi-matrix games," Research Memorandum 334, Tilburg University, Faculty of Economics and Business Administration.
  3. Talman, A.J.J. & Laan , G. van der, 1982. "On the computation of fixed points on the product space of unit simplices and an application to noncooperative N-person games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153028, Tilburg University.
  4. Van Den Elzen,A. & Talman,D., 1995. "An Algorithmic Approach Towards the Tracing Procedure of Harsanyi and Selten," Papers 95111, Tilburg - Center for Economic Research.
  5. Herings, P.J.J. & Talman, A.J.J. & Zang, Z., 1994. "The computation of a continuum of constrained equilibria," Discussion Paper 1994-38, Tilburg University, Center for Economic Research.
  6. van den Elzen, Antoon & Talman, Dolf, 1999. "An Algorithmic Approach toward the Tracing Procedure for Bi-matrix Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 130-145, July.
  7. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
  8. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
  9. Talman, A.J.J. & Laan , G. van der, 1980. "A new subdivision for computing fixed points with a homotopy algorithm," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153017, Tilburg University.
Full references (including those not matched with items on IDEAS)


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

Cited by:
  1. Keyzer, Michiel & van Wesenbeeck, Lia, 2005. "Equilibrium selection in games: the mollifier method," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 285-301, April.
  2. Klaus Abbink & Jordi Brandts, 0000. "24," Working Papers 62, Barcelona Graduate School of Economics.
    • Klaus Abbink & Jordi Brandts, 2002. "24," UFAE and IAE Working Papers 523.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Jordi Brandts & Klaus Abbink, 2004. "24," Levine's Bibliography 122247000000000073, UCLA Department of Economics.
  3. Herings, P. Jean-Jacques & Peeters, Ronald, 2006. "Homotopy Methods to Compute Equilibria in Game Theory," Research Memorandum 046, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Abbink, Klaus & Brandts, Jordi, 2008. "24. Pricing in Bertrand competition with increasing marginal costs," Games and Economic Behavior, Elsevier, vol. 63(1), pages 1-31, May.
  5. Wheatley, W. Parker, 2003. "Survival And Ownership Of Internet Marketplaces For Agriculture," 2003 Annual meeting, July 27-30, Montreal, Canada 22214, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
  6. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Claus-Jochen Haake & Francis Edward Su, 2006. "A simplicial algorithm approach to Nash equilibria in concave games," Working Papers 382, Bielefeld University, Center for Mathematical Economics.
  8. 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.
  9. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, EconWPA, revised 16 Oct 2003.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:dgr:kubcen:199804. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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