Constructive Application of the Linear Tracing Procedure to Polymatrix Games

Polymatrix games concern a class of noncooperative multiperson games in normal form.Characteristic for these games is that the payo s for any player are additive in the payo s obtained against the individual other players.Harsanyi and Selten (1988) developed the tracing procedure for selecting an equilibrium in general noncooperative games.However, its practical application may be cumbersome because of nonlinearities involved.In this paper we show that an adapted version of the algorithm developed by van den Elzen and Talman (1991) may serve as a nite method for computerizing the linear tracing procedure when applied to polymatrix games.The method works via complementary pivoting and generates a piecewise linear path.This path constitutes a projection of the path generated by the linear tracing procedure which is in general nonlinear.Stated in game-theoretic terms, the path generated by the pivoting procedure describes the adjustment of the beliefs underlying the linear tracing procedure.