Abstract
A modified Cournot oligopoly is introduced and examined in which the firms can treat their wastes up to a certain amount, and if the amount of waste is even higher then an outside facility is used with a given fixed cost and higher unit cost. The resulting payoff functions become discontinuous. The best response functions of firms are nonincreasing and also might be discontinuous. The best response functions can be modified to depend on the total industry output, which also might be discontinuous as well as multiple valued. The existence of at least one equilibrium is proved and numerical examples show the possibility of a unique equilibrium as well as that of multiple equilibria.
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References
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Acknowledgements
This paper has been prepared while the first author was a visiting professor at the Department of Economics of Chuo University, Tokyo, Japan. The authors highly appreciate the financial supports from the MEXT-Supported Program for the Strategic Research Foundation at Private Universities 2013–2017, the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) 24530202, 25380238 and 26380316) and Chuo University (Joint Research Grant). The usual disclaimers apply.
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Szidarovszky, F., Matsumoto, A. (2016). On a Discontinuous Cournot Oligopoly. In: von Mouche, P., Quartieri, F. (eds) Equilibrium Theory for Cournot Oligopolies and Related Games. Springer Series in Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-29254-0_8
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DOI: https://doi.org/10.1007/978-3-319-29254-0_8
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