A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method

This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method. ∗We are greatly indebted to Guy Arie, David Besanko, Paul Grieco, Ken Judd, Lauren Lu, Mark Satterthwaite, Karl Schmedders, Che-Lin Su, and Layne Watson for comments and suggestions. Borkovsky and Kryukov thank the General Motors Center for Strategy in Management at Northwestern’s Kellogg School of Management for support during this project. Doraszelski gratefully acknowledges financial support from the National Science Foundation under Grant No. 0615615. †Kellogg School of Management, Northwestern University, Evanston, IL 60208, [email protected]. ‡Department of Economics, Harvard University, Cambridge, MA 02138, [email protected]. §Department of Economics, Northwestern University, Evanston, IL 60208, [email protected].