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Price-Wars in Finite Sequential Move Price Competition: The Role of Discounting


  • Wallner, Klaus



This paper characterizes the unique Markov equilibrium in the sequential move, finite horizon pricing duopoly with discounting. Simple, short cycles repeat until the last two periods. For discount factors above 0.75488, there are three-period reaction function cycles and below 0.75488, two-period cycles. The equilibrium path in the latter case has continued marginal undercutting at high prices, followed by infrequent but regular price wars. In a price war, a firm lowers all the way to a trigger level low enough to induce the rival's raise in the price next period. While the price war is costly, both firms benefit in form of a higher market price in the following periods. Average long-run industry profits are bounded below by half the monopoly level, and are non-monotonic in the discount factor.

Suggested Citation

  • Wallner, Klaus, 2000. "Price-Wars in Finite Sequential Move Price Competition: The Role of Discounting," SSE/EFI Working Paper Series in Economics and Finance 374, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0374

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    More about this item


    Price wars; finite games; discounting; sequential moves;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets


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