Working Papers

Markov Quantal Response Equilibrium and a Homotopy Method for Computing and Selecting Markov Perfect Equilibria of Dynamic Stochastic Games
January 2019

With David Poensgen.
Link to Paper.

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. 


dsGameSolver: A Python Program for Computing Markov Perfect Equilibria of Dynamic Stochastic Games
January 2019

With David Poensgen.
Link to Paper.
Link to Program.

dsGameSolver is based on the homotopy method developed in Eibelshaeuser and Poensgen (2019). It is the first program capable of computing a Markov perfect equilibrium of any finite dynamic stochastic game -- subject to the usual restrictions on numerical accuracy and working memory. dsGameSolver supports general games with state-player-specific numbers of actions and individual discount factors, covering virtually any game of complete information. Furthermore, it is remarkably performant and able to handle games with thousands of state-player-actions. Finally, dsGameSolver allows users with basic programming skills in Python to formulate complex games with ease and to directly use the results for subsequent illustration and analysis. 


High-Frequency Price Fluctuations in Brick-and-Mortar Retailing
December 2018

With Sascha Wilhelm.
Link to Paper.
Media Coverage: n-tv Nachrichten (2019-06-07), HR Hessenschau (2019-04-19), RTL Extra (2019-04-17)ZDF Heute (2019-04-12)Rhein-Main Zeitungen (2019-12-29), Darmstädter Echo (2018-12-29)Focus Online (2018-12-12)Motorzeitung (2018-12-07), Goethe-Universität Frankfurt UniReport (2018-12-07)FAZ Woche (2017-06-24), FAZ Wirtschaft (2017-05-13).

The digital revolution of pricing enables retailers to change their prices more frequently than ever before. While the industry endorses this development, critics fear it could foster excessive price fluctuations. This paper studies price fluctuations in the context of brick-and-mortar retailing with business hours. First, we develop a model of dynamic price competition and show that intraday fluctuations in retail prices can emerge from strategic interaction among retailers alone, even in the absence of variation in wholesale prices and demand. Furthermore, the model makes detailed predictions concerning the shapes of pricing patterns. As a second step, we test and verify the model's predictions using an extensive dataset on the German retail gasoline market. Moreover, we calibrate the model and show that regulations aiming to curb price fluctuations can backfire.