Perpetual Leapfrogging in Bertrand Duopoly

Abstract

We consider different patterns of infinite technological adoption choices by firms in a Bertrand duopoly. Every period technological progress provides a sequence of cost reducing innovations. The equilibrium concept is Markov perfect equilibrium. We analyze conditions for which equilibrium adoption leads to persistent leadership and those where firms alternate in adoption inducing leapfrogging. Only leapfrogging leads to technological improvement in the long run. Demand conditions play a crucial role in determining whether leapfrogging can be perpetual in Bertrand duopoly.

Dynamic competition in technological investments: An empirical examination of the LCD panel industry

“…Hence, the followers will respond aggressively to a greater leader capacity in the "actionreaction" pattern a la Giovannetti (2001). This intuition is also consistent with earlier theoretical models of the R&D race (Fudenberg et al, 1983;Harris and Vickers, 1987;Lippman and McCardle, 1987;Aghion et al, 1997), for which the basic premise is that to remain effective contenders, the followers must not lag too far behind.…”

“…He finds that laggard firms display a robust tendency to catch up.9 This feature precisely fits the perpetual leapfrogging inGiovannetti (2001).10 In fact, these two sets of terms have been used interchangeably in the literature of R&D races. 11 LCD fabs are often resold to other LCD firms.…”

The Dynamics of Bertrand Price Competition With Cost‐reducing Investments

“…Giovannetti () advances the literature by showing that a particular type of leapfrogging—alternating adoptions—can be an equilibrium outcome in a discrete time duopoly model of Bertrand price competition under assumptions that are broadly similar to Riordan and Salant (). Though Giovannetti () does not cite or specifically address Riordan and Salant's () work, he shows that both preemption and alternating adoptions can be equilibrium outcomes depending on the elasticity of demand.…”

“…Giovannetti's () analysis is done in the context of a game where firms make simultaneous investment decisions, whereas Riordan and Salant () model the investment choices as an alternating move game. The alternating move assumption seems to be a reasonable way to approximate decisions made in continuous time, where it is unlikely that two firms would be informed of a new technological innovation and make investment decisions at precisely the same instant.…”

Leapfrogging cycles in international competition

“…For instance, the important paper by Giovannetti (2001) considers a duopoly in which …rms considering in…nite technological adoption set prices with Bertrand competition in the product market. Using this model, Giovannetti identi…es the conditions whereby …rms alternate in adopting the new technology, thereby representing a leapfrogging process.…”