Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games
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.
(This abstract was borrowed from another version of this item.)
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Mas-Colell,Andreu, 1985.
"The Theory of General Economic Equilibrium,"
Cambridge University Press, number 9780521265140.
- John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
- Herings, P.J.J. & Talman, A.J.J. & Zang, Z., 1994.
"The computation of a continuum of constrained equilibria,"
1994-38, Tilburg University, Center for Economic Research.
- Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1996. "The computation of a continuum of constrained equilibria," Other publications TiSEM ba4c6d83-befb-4a25-8477-c, Tilburg University, School of Economics and Management.
- van den Elzen, A.H., 1996. "Constructive Application of the Linear Tracing Procedure to Polymatrix Games," Research Memorandum 738, Tilburg University, School of Economics and Management.
- Talman, A.J.J. & van der Laan, G., 1982. "On the computation of fixed points on the product space of unit simplices and an application to noncooperative N-person games," Other publications TiSEM ba74b902-87c8-43d5-8471-6, Tilburg University, School of Economics and Management.
- Talman, A.J.J. & van der Laan, G., 1980. "A new subdivision for computing fixed points with a homotopy algorithm," Other publications TiSEM d702630e-5e0d-4c31-bd1e-1, Tilburg University, School of Economics and Management.
- Talman, A.J.J. & Doup, T.M., 1987. "A continuous deformation algorithm on the product space of unit simplices," Other publications TiSEM 0f7c777f-9ae5-4218-b3bd-2, Tilburg University, School of Economics and Management.
- Talman, A.J.J. & van den Elzen, A.H., 1991. "A procedure for finding Nash equilibria in bi-matrix games," Other publications TiSEM 14df3398-1521-43ad-8803-a, Tilburg University, School of Economics and Management.
- 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.
- Van Den Elzen,A. & Talman,D., 1995.
"An Algorithmic Approach Towards the Tracing Procedure of Harsanyi and Selten,"
95111, Tilburg - Center for Economic Research.
- van den Elzen, A.H. & Talman, A.J.J., 1995. "An algorithmic approach towards the tracing procedure of Harsanyi and Selten," Discussion Paper 1995-111, Tilburg University, Center for Economic Research.
- B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:38:y:2002:i:1:p:89-117. 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: (Zhang, Lei)
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.