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Entry, Exit, and Technological Progress in Markov-Perfect Duopoly

Author

Listed:
  • Abbring, Jaap
  • Campbell, Jeffrey
  • Yang, Nan

Abstract

This paper establishes the existence and essential uniqueness of an intuitively refined Markov-perfect equilibrium in a duopoly game with sunk costs, barriers to entry, firm-specific technological progress, and irreversible exit. We develop an algorithm that quickly computes the equilibrium by solving for fixed points of a finite sequence of auxiliary contraction mappings, which we label Fake Backward Induction. We illustrate the game’s practical value with a quantitative analysis of competition policy in a stochastically growing market with firms idiosyncratically learning by aging. Computing one equilibrium of this example takes 10.2 seconds on one Apple M5 Pro core.

Suggested Citation

  • Abbring, Jaap & Campbell, Jeffrey & Yang, Nan, 2026. "Entry, Exit, and Technological Progress in Markov-Perfect Duopoly," CEPR Discussion Papers 22071, Centre for Economic Policy Research.
    • Handle: RePEc:cpr:ceprdp:22071
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    File URL: https://cepr.org/publications/DP22071
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    Keywords

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    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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