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Computation of the Nash Equilibrium Selected by the Tracing Procedure in N-Person Games
Herings,P.J.J. van den Elzen,A.H.
Herings,P.J.J.
van den Elzen,A.H.
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.
Description
Pagination: 28
Date
1998
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Publisher
Microeconomics
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Keywords
Computation of equilibria, Non-cooperative game theory, Tracing procedure, C63 - Computational Techniques ; Simulation Modeling, C72 - Noncooperative Games
Citation
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, Tilburg.