The Logarithmic Stochastic Tracing Procedure: A Homotopy Method to Compute Stationary Equilibria of Stochastic Games
References
- (2018) Very simple Markov-perfect industry dynamics: Theory. Econometrica 86(2):721–735.Crossref, Google Scholar
- (2010) Learning-by-doing, organizational forgetting, and industry dynamics. Econometrica 78(2):453–508.Crossref, Google Scholar
- (1978) Finding zeroes of maps: Homotopy methods that are constructive with probability one. Math. Comput. 32(143):887–899.Crossref, Google Scholar
- (2022) An interior-point differentiable path-following method to compute stationary equilibria in stochastic games. INFORMS J. Comput. 34(3):1403–1418.Link, Google Scholar
- (2009) The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1):195–259.Crossref, Google Scholar
- (2012) Avoiding the curse of dimensionality in dynamic stochastic games. Quant. Econom. 3(1):53–93.Crossref, Google Scholar
- (2007) A framework for applied dynamic analysis in IO. Armstrong M, Porter RH, eds. Handbook of Industrial Organization, vol. 3 (Elsevier, Amsterdam), 1887–1966.Google Scholar
- (2010) Computable Markov-perfect industry dynamics. RAND J. Econom. 41(2):215–243.Crossref, Google Scholar
- (1999) General equilibrium models and homotopy methods. J. Econom. Dynamic Control 23(9):1249–1279.Crossref, Google Scholar
- (2020) Markov quantal response equilibrium and a homotopy method for computing and selecting stationary equilibria of stochastic games. Working paper, Goethe University Frankfurt, Frankfurt, Germany.Google Scholar
- (2023) sgamesolver: A Python package to solve stochastic games. Working paper, Goethe University Frankfurt, Frankfurt, Germany.Google Scholar
- (1995) Markov-perfect industry dynamics: A framework for empirical work. Rev. Econom. Stud. 62(1):53–82.Crossref, Google Scholar
- (1964) Equilibrium in a stochastic n-person game. J. Sci. Hiroshima Univ. Ser. A-I (Math.) 28(1):89–93.Google Scholar
- (1989) Nash and correlated equilibria: Some complexity considerations. Games Econom. Behav. 1(1):80–93.Crossref, Google Scholar
- (2005) Equilibrium in a dynamic limit order market. J. Finance 60(5):2149–2192.Crossref, Google Scholar
- (2009) A global Newton method for stochastic games. J. Econom. Theory 144(1):414–421.Crossref, Google Scholar
- (1975) The tracing procedure: A Bayesian approach to defining a solution for n-person noncooperative games. Internat. J. Game Theory 4(2):61–94.Crossref, Google Scholar
- (1988) A General Theory of Equilibrium Selection in Games (MIT Press, Cambridge, MA).Google Scholar
- (2003) Equilibrium selection in stochastic games. Internat. Game Theory Rev. 5(4):307–326.Crossref, Google Scholar
- (2004) Stationary equilibria in stochastic games: Structure, selection, and computation. J. Econom. Theory 118(1):32–60.Crossref, Google Scholar
- (1980) On a class of systems of transcendental equations. Soviet Math. Doklady 22(3):762–765.Google Scholar
- (1986) On the strategic stability of equilibria. Econometrica 54(5):1003–1037.Crossref, Google Scholar
- (1980) The great fish war: An example using a dynamic Cournot-Nash solution. Bell J. Econom. 11(1):322–334.Crossref, Google Scholar
- (1996) Model theory and exponentiation. Notices Amer. Math. Soc. 43(7):753–759.Google Scholar
- (1988a) A theory of dynamic oligopoly I: Overview and quantity competition with large fixed costs. Econometrica 56(3):549–569.Crossref, Google Scholar
- (1988b) A theory of dynamic oligopoly II: Price competition, kinked demand curves, and Edgeworth cycles. Econometrica 56(3):571–599.Crossref, Google Scholar
- (1995) Quantal response equilibria for normal form games. Games Econom. Behav. 10(1):6–38.Crossref, Google Scholar
- (1995) Unraveling in guessing games: An experimental study. Amer. Econom. Rev. 85(5):1313–1326.Google Scholar
- (1994) Computing Markov perfect Nash equilibria: Numerical implications of a dynamic differentiated product model. RAND J. Econom. 25(4):555–589.Crossref, Google Scholar
- (1998) Modern Simulation and Modeling (Wiley, New York).Google Scholar
- (1976) Principles of Mathematical Analysis, 3rd ed. (McGraw-Hill, New York).Google Scholar
- (1991) The algebraic geometry of games and the tracing procedure. Selten R, ed. Game Equilibrium Models II: Methods, Morals, and Markets (Springer, Heidelberg, Germany), 9–43.Crossref, Google Scholar
- (1953) Stochastic games. Proc. Natl. Acad. Sci. USA 39(10):1095–1100.Crossref, Google Scholar
- (2015) Stochastic games. Proc. Natl. Acad. Sci. USA 112(45):13743–13746.Crossref, Google Scholar
- (1995) On players’ models of other players: Theory and experimental evidence. Games Econom. Behav. 10(1):218–254.Crossref, Google Scholar
- (1964) Equilibrium points of stochastic, noncooperative n-person games. J. Sci. Hiroshima Univ. Ser. A-I (Math.) 28(1):95–99.Google Scholar
- (2002) Probability-one homotopies in computational science. J. Comput. Appl. Math. 140(1–2):785–807.Crossref, Google Scholar
- (1981) Pathways to Solutions, Fixed Points, and Equilibria (Prentice-Hall, Upper Saddle River, NJ).Google Scholar

