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
Date Written: January 10, 2019
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: Suggested Citation