The Dynamics of Bertrand Price Competition with Cost-Reducing Investments
58 Pages Posted: 13 Jun 2013
There are 2 versions of this paper
The Dynamics of Bertrand Price Competition with Cost-Reducing Investments
The Dynamics of Bertrand Price Competition with Cost‐Reducing Investments
Date Written: March 15, 2013
Abstract
We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars”. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly” equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.
Keywords: duopoly, Bertrand-Nash price competition, Bertrand paradox, Bertrand investment paradox, leapfrogging, cost-reducing investments, technological improvement, dynamic models of competition, Markov-perfect equilibrium, tacit collusion, price wars, coordination and anti-coordination games, strategic
JEL Classification: D92, L11, L13
Suggested Citation: Suggested Citation
Here is the Coronavirus
related research on SSRN
Recommended Papers
-
Estimating Dynamic Models of Imperfect Competition
By Patrick Bajari, C. Lanier Benkard, ...
-
Estimating Dynamic Models of Imperfect Competition
By Patrick Bajari, C. Lanier Benkard, ...
-
Sequential Estimation of Dynamic Discrete Games
By Victor Aguirregabiria and Pedro Mira
-
By Ariel Pakes and Paul Mcguire
-
Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Examples)
By Ariel Pakes, Michael Ostrovsky, ...
-
Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)
By Ariel Pakes, Michael Ostrovsky, ...
-
A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft
-
Multiple Equilibria and Deterrence in Airline Markets
By Federico Ciliberto and Zhou Zhang
-
Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity
-
Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity
