The Logarithmic Stochastic Tracing Procedure: A Homotopy Method for Computing and Selecting Stationary Equilibria of Stochastic Games
42 Pages Posted: 12 Feb 2021 Last revised: 10 Jul 2022
Date Written: July 9, 2022
Abstract
This paper develops the logarithmic stochastic tracing procedure for finite discounted stochastic games. 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 that gradually transform priors into equilibrium beliefs. Harsanyi and Selten interpret this as a process of strategic Bayesian reasoning, making it a well-founded tool for equilibrium selection. We prove two main results: First, there exists a unique solution path which is smooth, interior, isolated, and of finite length. Second, the limiting solution path is consistent with the linear procedure whenever the latter is well-defined. Our method allows the computation of stationary equilibria of any stochastic game via homotopy continuation; a ready-to-use implementation is publicly available.
Keywords: Stochastic game, Tracing, Homotopy method, Equilibrium computation, Equilibrium selection
JEL Classification: C73, C63
Suggested Citation: Suggested Citation