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Computation of the Nash equilibrium selected by the tracing procedure in n-person games

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Author Info
Herings, P.J.J.
Elzen, A. van den (Tilburg University, Center for Economic Research)

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Abstract

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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 4.

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Date of creation: 1998
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Handle: RePEc:dgr:kubcen:19984

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

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  1. Elzen, A. van den, 1996. "Constructive application of the linear tracing procedure to polymatrix games," Research Memorandum 738, Tilburg University, Faculty of Economics and Business Administration. [Downloadable!]
  2. Damme, E. van, 1995. "Game Theory : The Next Stage," Discussion Paper 73, Tilburg University, Center for Economic Research. [Downloadable!]
  3. 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.
  4. Herings, P. Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1996. "The Transition from a Drèze Equilibrium to a Walrasian Equilibrium," Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) Discussion Paper 1996013, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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(explanations, 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. 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). [Downloadable!]
  2. Kolen Antoon, 2006. "A genetic algorithm for the partial binary constraint satisfaction problem: an application to a frequency assignment problem," Research Memoranda 045, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  3. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, EconWPA, revised 16 Oct 2003. [Downloadable!]
  4. Herings,P. Jean-Jacques & Peeters,Ronald J.A.P, 2000. "Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation," Research Memoranda 004, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  5. Jordi Brandts & Klaus Abbink, 2004. "24," Levine's Bibliography 122247000000000073, UCLA Department of Economics. [Downloadable!]
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