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Constructive application of the linear tracing procedure to polymatrix games

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Author Info
Elzen, A. van den (Tilburg University, Faculty of Economics and Business Administration)
Abstract

Polymatrix games concern a class of noncooperative multiperson games in normal form. Characteristic for these games is that the payo s for any player are additive in the payo s obtained against the individual other players. Harsanyi and Selten (1988) developed the tracing procedure for selecting an equilibrium in general noncooperative games. However, its practical application may be cumbersome because of nonlinearities involved. In this paper we show that an adapted version of the algorithm developed by van den Elzen and Talman (1991) may serve as a nite method for computerizing the linear tracing procedure when applied to polymatrix games. The method works via complementary pivoting and generates a piecewise linear path. This path constitutes a projection of the path generated by the linear tracing procedure which is in general nonlinear. Stated in game-theoretic terms, the path generated by the pivoting procedure describes the adjustment of the beliefs underlying the linear tracing procedure.

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Paper provided by Tilburg University, Faculty of Economics and Business Administration in its series Research Memorandum with number 738.

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Date of creation: 1996
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Handle: RePEc:dgr:kubrem:1996738

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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.:
  1. 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, December.
  2. Gowda, M Seetharama & Sznajder, Roman, 1996. "A Generalization of the Nash Equilibrium Theorem on Bimatrix Games," International Journal of Game Theory, Springer, vol. 25(1), pages 1-12.
  3. Quintas, L G, 1989. "A Note on Polymatrix Games," International Journal of Game Theory, Springer, vol. 18(3), pages 261-72.
  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. Talman, Dolf & Elzen van den, A.H., 1991. "A procedure for finding Nash equilibria in bi-matrix games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153117, Tilburg University. [Downloadable!]
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  1. Herings, P.J.J. & Elzen, A. van den, 1998. "Computation of the Nash equilibrium selected by the tracing procedure in n-person games," Discussion Paper 4, Tilburg University, Center for Economic Research. [Downloadable!]
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