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Product Pricing when Demand Follows a Rule of Thumb

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  • Christina Matzke

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  • Benedikt Wirth
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    Abstract

    We analyze the strategic behavior of firms when demand is determined by a rule of thumb behavior of consumers. We assume consumer dynamics where individual consumers follow simple behavioral decision rules governed by imitation and habit as suggested in consumer research. On this basis, we investigate monopoly and competition between firms, described via an open-loop differential game which in this setting is equivalent to but analytically more convenient than a closed-loop system. We derive a Nash equilibrium and examine the influence of advertising. We show for the monopoly case that a reduction of the space of all price paths in time to the space of time-constant prices is sensible since the latter in general contains Nash equilibria. We prove that the equilibrium price of the weakest active firm tends to marginal cost as the number of (non-identical) firms grows. Our model is consistent with observed market behavior such as product life cycles.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse3_2009.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse3_2009.

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    Length: 37
    Date of creation: Feb 2009
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse3_2009

    Contact details of provider:
    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: bounded rationality; social learning; population game; differential game; product life cycle; monopoly; competition; pricing; advertising;

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    References

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    1. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
    2. Sandholm, William H., 2005. "Excess payoff dynamics and other well-behaved evolutionary dynamics," Journal of Economic Theory, Elsevier, vol. 124(2), pages 149-170, October.
    3. Stigler, George J & Becker, Gary S, 1977. "De Gustibus Non Est Disputandum," American Economic Review, American Economic Association, vol. 67(2), pages 76-90, March.
    4. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
    5. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
    6. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
    7. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
    8. Pingle, Mark & Day, Richard H., 1996. "Modes of economizing behavior: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 29(2), pages 191-209, March.
    9. Smallwood, Dennis E & Conlisk, John, 1979. "Product Quality in Markets Where Consumers are Imperfectly Informed," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 1-23, February.
    10. Heaton, John, 1993. "The Interaction between Time-Nonseparable Preferences and Time Aggregation," Econometrica, Econometric Society, vol. 61(2), pages 353-85, March.
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