The Continuous Logit Dynamic and Price Dispersion

34 Pages Posted: 3 Sep 2014 Last revised: 8 Nov 2014

See all articles by Ratul Lahkar

Ratul Lahkar

Ashoka University - Department of Economics

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Date Written: August 5, 2014

Abstract

We define the logit dynamic for games with continuous strategy spaces and establish its fundamental properties, i.e. the existence, uniqueness and continuity of solutions. We apply the dynamic to the analysis of the Burdett and Judd (1983) model of price dispersion. Our objective is to assess the stability of the logit equilibrium corresponding to the unique Nash equilibrium of this model. Although a direct analysis of local stability is difficult due to technical difficulties, an appeal to finite approximation techniques suggest that the logit equilibrium is unstable. Price dispersion, instead of being an equilibrium phenomenon, is a cyclical phenomenon. We also establish a result on the Lyapunov stability of logit equilibria in negative definite games.

Keywords: Price dispersion, Evolutionary game theory, Logit dynamic

JEL Classification: C72, C73, L11

Suggested Citation

Lahkar, Ratul and Riedel, Frank, The Continuous Logit Dynamic and Price Dispersion (August 5, 2014). Institute of Mathematical Economics Working Paper No. 521, Available at SSRN: https://ssrn.com/abstract=2490440 or http://dx.doi.org/10.2139/ssrn.2490440

Ratul Lahkar

Ashoka University - Department of Economics ( email )

Plot #2,
Rajiv Gandhi Education City
Kundli, 131028
India

Frank Riedel (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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