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An algorithmic approach toward the tracing procedure for bi-matrix games. (English) Zbl 0939.91006

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.

MSC:

91A05 2-person games
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[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
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