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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. 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.
  2. 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!]
  3. Damme, E. van, 1995. "Game Theory : The Next Stage," Discussion Paper 73, Tilburg University, Center for Economic Research. [Downloadable!]
  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. Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1996. "The Transition from a Drze Equilibrium to a Walrasian Equilibrium," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996013, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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  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. 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). [Downloadable!]
  3. 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!]
  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!]
  6. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, EconWPA, revised 16 Oct 2003. [Downloadable!]
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