An Algorithmic Approach toward the Tracing Procedure for Bi-matrix Games

Abstract 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 we 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 our procedure with lexicographic pivoting we obtain an always well-defined alternative for the logarithmic tracing procedure which is difficult to implement. Journal of Economic Literature Classification Numbers: C63, C72.