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A Dynamic Model of Leap-Frogging Investments and Bertrand Price Competition


  • John Rust

    (University of Maryland)

  • Bertel Schjerning

    (University of Copenhagen)

  • Fedor Iskhakov

    (University of Technology Sydney)


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 and attain, at least temporarily, low-cost leadership. The model resolves a paradox about investing in the presence of Bertrand price competition: if both firms simultaneously invest in the current state-of-the-art production technology and thereby attain the same marginal cost of production, the resulting price competition drives the price down to marginal cost and profits to zero. Thus, it would seem that neither firm can profit from undertaking the cost-reducing investment, so the firms should not have any incentive to undertake cost-reducing investments if they are Bertrand price competitors. We show this simple intuition is incorrect. We formulate a dynamic model of price and investment competition as a Markov-perfect equilibrium to a dynamic game. We show that even when firms start with the same marginal costs of production there are equilibria where one of the firms invests first, and leapfrogs its opponent. In fact, there are many equilibria, with some equilibria exhibiting asymmetries where there are extended periods of time where only one of the firms does most of the investing, and other equilibria where there are alternating investments by the two firms as they vie for temporary low cost leadership. Our model provides a new interpretation of the concept of a "price war". Instead of being a sign of a breakdown of tacit collusion, in our model price wars occur when one firm leapfrogs its opponent to become the new low cost leader.

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  • John Rust & Bertel Schjerning & Fedor Iskhakov, 2012. "A Dynamic Model of Leap-Frogging Investments and Bertrand Price Competition," 2012 Meeting Papers 370, Society for Economic Dynamics.
  • Handle: RePEc:red:sed012:370

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    References listed on IDEAS

    1. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
    2. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    3. Rust, John, 1986. "When Is It Optimal to Kill Off the Market for Used Durable Goods?," Econometrica, Econometric Society, vol. 54(1), pages 65-86, January.
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