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The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

Author

Listed:
  • Fedor Iskhakov

    (CEPAR, University of New South Wales)

  • John Rust

    (Georgetown University)

  • Bertel Schjerning

    (University of Copenhagen)

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.

Suggested Citation

  • Fedor Iskhakov & John Rust & Bertel Schjerning, 2013. "The Dynamics of Bertrand Price Competition with Cost-Reducing Investments," Discussion Papers 13-05, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:1305
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    References listed on IDEAS

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    Cited by:

    1. Ulrich Doraszelski & Kenneth L. Judd, 2019. "Dynamic stochastic games with random moves," Quantitative Marketing and Economics (QME), Springer, vol. 17(1), pages 59-79, March.
    2. Fedor Iskhakov & John Rust & Bertel Schjerning, 2016. "Recursive Lexicographical Search: Finding All Markov Perfect Equilibria of Finite State Directional Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 83(2), pages 658-703.
    3. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    4. Jacob Seifert, 2015. "Welfare effects of compulsory licensing," Journal of Regulatory Economics, Springer, vol. 48(3), pages 317-350, December.
    5. Ronald Goettler & Brett Gordon, 2014. "Competition and product innovation in dynamic oligopoly," Quantitative Marketing and Economics (QME), Springer, vol. 12(1), pages 1-42, March.

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    More about this item

    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 preemption;
    All these keywords.

    JEL classification:

    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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