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Price-taking Strategy Versus Dynamic Programming in Oligopoly

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Author Info

  • HUANG Weihong

    (Division of Economics,School of Humanities and Social Sciences, Nanyang Technological University, Singapore
    Nanyang Technological University, Singapore)

Abstract

In a quantity-competed duopoly, one firm is a naive price-taker (who responses only to the last period’s price) while the other has all the market information so as be able to optimize its profit stream (either discounted or un-discounted) dynamically over a finite or infinite horizon. With a traditional linear economy, we are able to derive algebraically the optimal policies of all periods for the dynamic optimizer. A counter-intuitive phenomenon is then observed: regardless of the planning horizon and the discounted factor, there exists a relative profitability range of initial prices, starting with which the price-taker make higher profit than the dynamic optimizer. Furthermore, with the increase in the planning horizon, the price-taker’s relative profitability range increases accordingly and finally covers the entire economically meaningful range.

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Bibliographic Info

Paper provided by Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre in its series Economic Growth centre Working Paper Series with number 0904.

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Length: 18 pages
Date of creation: Apr 2009
Date of revision:
Handle: RePEc:nan:wpaper:0904

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Related research

Keywords: Economics; dynamic programming; Bellman’s optimality principle; applied OR; duopoly;

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  1. Cyert, Richard M & DeGroot, M H, 1970. "Multiperiod Decision Models with Alternating Choice as a Solution to the Duopoly Problem," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 410-29, August.
  2. Huang, Weihong, 2008. "The long-run benefits of chaos to oligopolistic firms," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1332-1355, April.
  3. Haurie, A., 1976. "Optimal control on an infinite time horizon : The turnpike approach," Journal of Mathematical Economics, Elsevier, vol. 3(1), pages 81-102, March.
  4. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
  5. Dana, Rose-Anne & Montrucchio, Luigi, 1987. "On rational dynamic strategies in infinite horizon models where agents discount the future," Journal of Economic Behavior & Organization, Elsevier, vol. 8(3), pages 497-511, September.
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