To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time a la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton-Jacobi-Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand. (C) 2013 Elsevier B.V. All rights reserved.

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation / Luca, Lambertini; Palestini, Arsen. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - STAMPA. - 236:1(2014), pp. 272-281. [10.1016/j.ejor.2013.12.008]

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

PALESTINI, Arsen
2014

Abstract

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time a la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton-Jacobi-Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand. (C) 2013 Elsevier B.V. All rights reserved.
2014
hamilton-jacobi- bellman equation; differential game; markov-perfect equilibrium; horizontal mergers; capacity
01 Pubblicazione su rivista::01a Articolo in rivista
On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation / Luca, Lambertini; Palestini, Arsen. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - STAMPA. - 236:1(2014), pp. 272-281. [10.1016/j.ejor.2013.12.008]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/535599
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