Abstract
Discretely-constrained Nash-Cournot games have attracted attention as they arise in various competitive energy production settings in which players must make one or more discrete decisions. Gabriel et al. (Netw Spat Econ 13(3):307–326 2013) claim that the set of equilibria to a discretely-constrained Nash-Cournot game coincides with the set of solutions to a corresponding discretely-constrained mixed complementarity problem. We show that one direction of this claim is false by providing counterexamples to show that there exist solutions to the discretely-constrained Nash-Cournot game that do not coincide with solutions to the discretely-constrained mixed complementarity problem. The updated theorem in this note formally states that every solution to the discretely-constrained mixed complementarity problem is a solution to the discretely-constrained Nash-Cournot game, but not vice versa.
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We thank Myun-Seok Cheon and two anonymous referees for helpful suggestions that improved the quality of this note.
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Papageorgiou, D.J., Trespalacios, F. & Harwood, S. A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity. Netw Spat Econ 21, 325–330 (2021). https://doi.org/10.1007/s11067-021-09524-x
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DOI: https://doi.org/10.1007/s11067-021-09524-x