The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

This paper is co-authored with Fedor Iskhakov and John Rust. Revision requested by International Economic Review

A preprint of the paper can be found at Bertel Schjerning's web-page.

Abstract

We extend the classic Bertrand duopoly model of price competition to a dynamic setting with uncertain technological progress, where competing duopolists can undertake cost reducing investments in an attempt to leapfrog their rival to attain temporary low cost leadership.

We analytically characterize the set of all Markov perfect equilibria of this game, which include investment preemption where only one of the firms does all of the investing as well as leapfrogging with piece-wise flat equilibrium price paths punctuated by occasional discontinuous price declines that occur when one firm leapfrogs its rival.

Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient due to excessively frequent and duplicative investments.