Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games

P.J.J. Herings, A.H. van den Elzen

Research output: Working paperDiscussion paperOther research output

286 Downloads (Pure)

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.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages28
Volume1998-04
Publication statusPublished - 1998

Publication series

NameCentER Discussion Paper
Volume1998-04

Keywords

  • Computation of equilibria
  • Non-cooperative game theory
  • Tracing procedure

Fingerprint Dive into the research topics of 'Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games'. Together they form a unique fingerprint.

  • Cite this

    Herings, P. J. J., & van den Elzen, A. H. (1998). Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games. (CentER Discussion Paper; Vol. 1998-04). Microeconomics.