The Logarithmic Stochastic Tracing Procedure: A Homotopy Method for Computing and Selecting Stationary Equilibria of Stochastic Games

Abstract

This paper presents the logarithmic stochastic tracing procedure, a homotopy method for the computation and selection of stationary equilibria of any finite discounted stochastic game. It generalizes both the logarithmic tracing procedure (Harsanyi and Selten, 1988), which is defined only for normal form games, and the linear stochastic tracing procedure (Herings and Peeters, 2004), which is guaranteed to be well-defined only for generic games. Similar in spirit, our method defines a family of auxiliary games from prior beliefs; a path of equilibria of these is traversed until an equilibrium of the original game is reached. Harsanyi and Selten interpret this process as one of strategic Bayesian reasoning, in which priors are gradually transformed into equilibrium beliefs. This interpretation also applies to our procedure, making it a suitable tool for equilibrium selection. Because existence of a smooth, interior, and isolated solution path is guaranteed, the present algorithm is well-suited for the computation of stationary equilibria via numerical continuation methods. A ready-to-use implementation is publicly available; we report computational performance in this paper.