Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games

27 Pages Posted: 21 Jan 2019

See all articles by Steffen Eibelshäuser

Steffen Eibelshäuser

Goethe University Frankfurt, Department of Management and Applied Microeconomics

David Poensgen

Goethe University Frankfurt, Department of Management and Applied Microeconomics

Date Written: January 10, 2019

Abstract

We formally define Markov quantal response equilibrium (QRE) and prove existence for all finite discounted dynamic stochastic games. The special case of logit Markov QRE constitutes a mapping from precision parameter λ to sets of logit Markov QRE. The limiting points of this correspondence are shown to be Markov perfect equilibria. Furthermore, the logit Markov QRE correspondence can be given a homotopy interpretation. We prove that for all games, this homotopy contains a branch connecting the unique solution at λ = 0 to a unique limiting Markov perfect equilibrium. This result can be leveraged both for the computation of Markov perfect equilibria, and also as a selection criterion.

Keywords: Homotopy continuation, Stationary equilibrium, Logit choice

JEL Classification: C63, C73

Suggested Citation

Eibelshäuser, Steffen and Poensgen, David, Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games (January 10, 2019). Available at SSRN: https://ssrn.com/abstract=3314404 or http://dx.doi.org/10.2139/ssrn.3314404

Steffen Eibelshäuser (Contact Author)

Goethe University Frankfurt, Department of Management and Applied Microeconomics ( email )

Germany

David Poensgen

Goethe University Frankfurt, Department of Management and Applied Microeconomics ( email )

Germany

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