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.
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- 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.
- van den Elzen, A.H. & Talman, A.J.J., 1995.
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1995-111, Tilburg University, Center for Economic Research.
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- B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
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ba4c6d83-befb-4a25-8477-c, Tilburg University, School of Economics and Management.
- 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.
- 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.
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- 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.
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