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Oligopoly with Hyperbolic Demand: A Differential Game Approach

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  • L. Lambertini

Abstract

It is well known that the equilibrium solution of oligopoly games with isoelastic demand functions can be indeterminate. I revisit this issue through an open-loop differential game approach based on the assumption of sticky prices, to show that indeterminacy arises only in steady state, in the limit case where marginal costs tend to zero. Otherwise, at any time during the game, Pontryagin’s Maximum Principle ensures the existence of a unique and well defined solution, irrespective of the size of marginal costs. Finally, I show that an analogous result holds in the feedback case, although the Bellman equation of the representative firm cannot be solved analytically.

Suggested Citation

  • L. Lambertini, 2007. "Oligopoly with Hyperbolic Demand: A Differential Game Approach," Working Papers 597, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:597
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    1. McKelvey, Richard D. & Patty, John W., 2006. "A theory of voting in large elections," Games and Economic Behavior, Elsevier, vol. 57(1), pages 155-180, October.
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    3. Steffen Huck & Vicki Knoblauch & Wieland Müller, 2006. "Spatial Voting with Endogenous Timing," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 162(4), pages 557-570, December.
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    5. Patty, John Wiggs, 2005. "Local equilibrium equivalence in probabilistic voting models," Games and Economic Behavior, Elsevier, vol. 51(2), pages 523-536, May.
    6. repec:cup:apsrev:v:86:y:1992:i:04:p:929-937_09 is not listed on IDEAS
    7. Lambertini, Luca, 1997. "Optimal Fiscal Regime in a Spatial Duopoly," Journal of Urban Economics, Elsevier, vol. 41(3), pages 407-420, May.
    8. Kollman, Ken & Miller, John H. & Page, Scott E., 1997. "Landscape formation in a spatial voting model," Economics Letters, Elsevier, vol. 55(1), pages 121-130, August.
    9. Adams, James, 1999. "Policy Divergence in Multicandidate Probabilistic Spatial Voting," Public Choice, Springer, vol. 100(1-2), pages 103-122, July.
    10. Norman Schofield, 2006. "Equilibria in the spatial stochastic model of voting with party activists," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 183-203, December.
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