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On the Feedback Solution of a Differential Oligopoly Game with Hyperbolic Demand and Capacity Accumulation

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  • L. Lambertini

Abstract

I characterise the subgame perfect equilibrium of a differential market game with hyperbolic demand where firms are quantity-setters and accumulate capacity over time la Ramsey. I show that the open-loop solution is subgame perfect. Then, I analyse the feasibility of horizontal mergers, and compare the result generated by the dynamic setup with the merger incentive associated with the static model. It appears that allowing for the role of time makes mergers more likely to occur than they would on the basis of the static setting.

Suggested Citation

  • L. Lambertini, 2010. "On the Feedback Solution of a Differential Oligopoly Game with Hyperbolic Demand and Capacity Accumulation," Working Papers 692, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:692
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    References listed on IDEAS

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    1. Farrell, Joseph & Shapiro, Carl, 1988. "Horizontal Mergers: An Equilibrium Analysis," Department of Economics, Working Paper Series qt0tp305nx, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    2. Caputo, Michael R., 2007. "The envelope theorem for locally differentiable Nash equilibria of finite horizon differential games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 198-224, November.
    3. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
    4. Stephen W. Salant & Sheldon Switzer & Robert J. Reynolds, 1983. "Losses From Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 185-199.
    5. L. Lambertini, 2010. "Oligopoly with Hyperbolic Demand: A Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 108-119, April.
    6. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
    7. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
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    10. R. Cellini & L. Lambertini, 2008. "Weak and Strong Time Consistency in a Differential Oligopoly Game with Capital Accumulation," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 17-26, July.
    11. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    12. Perry, Martin K & Porter, Robert H, 1985. "Oligopoly and the Incentive for Horizontal Merger," American Economic Review, American Economic Association, vol. 75(1), pages 219-227, March.
    13. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, September.
    14. Hassan Benchekroun, 2003. "The closed‐loop effect and the profitability of horizontal mergers," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(3), pages 546-565, August.
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    Cited by:

    1. Kort, Peter M. & Wrzaczek, Stefan, 2015. "Optimal firm growth under the threat of entry," European Journal of Operational Research, Elsevier, vol. 246(1), pages 281-292.

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    More about this item

    JEL classification:

    • 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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