Oligopoly with Hyperbolic Demand: A Differential Game Approach

Lambertini, Luca ; Nitze, Paul H. (2007) Oligopoly with Hyperbolic Demand: A Differential Game Approach. Bologna: Dipartimento di Scienze economiche DSE, p. 16. DOI 10.6092/unibo/amsacta/4685. In: Quaderni - Working Paper DSE (597). ISSN 2282-6483.
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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.

Abstract
Document type
Monograph (Working Paper)
Creators
CreatorsAffiliationORCID
Lambertini, Luca
Nitze, Paul H.
Keywords
optimal control, differential games, Cournot competition, sticky prices
Subjects
ISSN
2282-6483
DOI
Deposit date
26 Feb 2016 11:10
Last modified
26 Feb 2016 11:10
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