van den Elzen, Antoon; Talman, Dolf An algorithmic approach toward the tracing procedure for bi-matrix games. (English) Zbl 0939.91006 Games Econ. Behav. 28, No. 1, 130-145 (1999). Summary: The main subroutines in the equilibrium selection theory of Harsanyi and Selten (1988) concern the linear and logarithmic tracing procedures which convert a given prior into an equilibrium. First, the authors show that for bi-matrix games the linear tracing procedure is equivalent, up to projection, to the pivoting procedure of the authors (1991), which enables implementation on a computer. Consequently, the linear tracing procedure, if well defined, generates a perfect equilibrium whenever it is started from a completely mixed prior. Finally, by applying their procedure with lexicographic pivoting they obtain an always well-defined alternative for the logarithmic tracing procedure which is difficult to implement. Cited in 8 Documents MSC: 91A05 2-person games Keywords:tracing procedure; equilibrium selection; complementary pivoting; homotopy; computation PDFBibTeX XMLCite \textit{A. van den Elzen} and \textit{D. Talman}, Games Econ. Behav. 28, No. 1, 130--145 (1999; Zbl 0939.91006) Full Text: DOI References: [1] Damme, E. E.C.van, Stability and Perfection of Nash Equilibria (1991), Springer-Verlag: Springer-Verlag Berlin · Zbl 0833.90126 [2] Elzen, A. H.van den; Talman, A. J.J., A procedure for finding Nash equilibria in bi-matrix games, ZOR-Methods Models Oper. Res., 35, 27-43 (1991) · Zbl 0729.90093 [3] Harsanyi, J. C., The tracing procedure: a Bayesian approach to defining a solution for \(n\)-person noncooperative games, Int. J. Game Theory, 4, 61-94 (1975) · Zbl 0319.90078 [4] Harsanyi, J. C., A solution concept for \(n\)-person noncooperative games, International Journal of Game Theory, 5, 211-225 (1976) · Zbl 0354.90097 [5] Harsanyi, J. C.; Selten, R., A General Theory of Equilibrium Selection in Games (1988), MIT Press: MIT Press Cambridge · Zbl 0693.90098 [6] Laan, G.van der; Talman, A. J.J., On the computation of fixed points in the product space of unit simplices and an application to noncooperative \(N\)-person games, Math. Oper. Res., 7, 1-13 (1982) · Zbl 0497.90063 [7] Schanuel, S. H.; Simon, L. K.; Zame, W. R., The algebraic geometry of games and the tracing procedure, (Selten, R., Game Equilibrium Models II: Methods, Morals and Markets (1991), Springer-Verlag: Springer-Verlag Berlin), 9-42 · Zbl 0813.90134 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.