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Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

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Abstract

A Nash–Cournot model for oligopolistic markets with concave cost functions and a differentiated commodity is analyzed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity assumptions. The results of some numerical tests on randomly generated markets are also reported.

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Acknowledgements

We would like to thank Marco Castellani and Massimiliano Giuli for providing background material for the proof of Theorem 4(a). The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA - National Group for Mathematical Analysis, Probability and their Applications) of the Istituto Nazionale di Alta Matematica (INdAM - National Institute of Higher Mathematics).

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  1. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Giancarlo Bigi & Mauro Passacantando

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  1. Giancarlo Bigi
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  2. Mauro Passacantando
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Correspondence to Giancarlo Bigi.

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Bigi, G., Passacantando, M. Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities. Decisions Econ Finan 40, 63–79 (2017). https://doi.org/10.1007/s10203-017-0187-7

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