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Imitators and Optimizers in a Changing Environment

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  • Burkhard Hehenkamp
  • Oddvar Kaarbøe

Abstract

We analyze the dynamic interaction between imitators and optimizers in a changing world. To this end, we put forward a symmetric duopoly game of strategic substitutes where players interact repeatedly in a world of demand- and cost-uncertainty. If the environment changes every period, the process converges globally to a unique two-period cycle where the optimizer has highest payoff every period. As to the general stochastic case, we characterize the long-run average per-period payoff for the optimizer and the imitator respectively as a function of the environmental switching probabilities. It turns out that the imitator experiences selection pressure for a large range of switching probabilities.

Suggested Citation

  • Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics 02_01, University of Dortmund, Department of Economics.
  • Handle: RePEc:mik:wpaper:02_01
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    References listed on IDEAS

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    1. Gale, Douglas & Rosenthal, Robert W., 1999. "Experimentation, Imitation, and Stochastic Stability," Journal of Economic Theory, Elsevier, vol. 84(1), pages 1-40, January.
    2. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    3. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    4. Rhode, Paul & Stegeman, Mark, 2001. "Non-Nash equilibria of Darwinian dynamics with applications to duopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 415-453, March.
    5. Schenk-Hoppe, Klaus Reiner, 2000. "The evolution of Walrasian behavior in oligopolies," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 35-55, February.
    6. Gale, Douglas & Rosenthal, Robert W., 2001. "Experimentation, Imitation, and Stochastic Stability: Addendum," Journal of Economic Theory, Elsevier, vol. 97(1), pages 164-174, March.
    7. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    8. Conlisk, John, 1980. "Costly optimizers versus cheap imitators," Journal of Economic Behavior & Organization, Elsevier, vol. 1(3), pages 275-293, September.
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    Citations

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    Cited by:

    1. Schipper, Burkhard C., 2009. "Imitators and optimizers in Cournot oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1981-1990, December.
    2. Khan, Abhimanyu & Peeters, Ronald, 2015. "Imitation by price and quantity setting firms in a differentiated market," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 28-36.
    3. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
    4. Fosco, Constanza & Mengel, Friederike, 2011. "Cooperation through imitation and exclusion in networks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(5), pages 641-658, May.
    5. Matros, Alexander, 2012. "Altruistic versus egoistic behavior in a Public Good game," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 642-656.
    6. Tsakas, Nikolas, 2015. "Beatable imitation in symmetric games with perturbed payoffs," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 34-40.
    7. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 1112, University of California, Davis, Department of Economics.
    8. Schipper, Burkhard C, 2011. "Strategic control of myopic best reply in repeated games," MPRA Paper 30219, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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