Stability and instability in oligopoly |
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| Authors: | Dave Furth |
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| Affiliation: | 1. Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia;2. Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;3. CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Slovenia;4. Faculty of Medicine, University of Maribor, Slovenia;1. Department of Radiation Oncology, Massachusetts General Hospital, Boston, Massachusetts;2. Retired;3. Paul Scherrer Institut, Villigen, Switzerland |
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| Abstract: | For regular oligopolies (both homogeneous and heterogeneous) the (local) Cournot-Nash equilibria are the (non-degenerate) critical points of a Morse-Smale vector field, defined on the feasible region of non-negative prices and outputs. When at the boundary of this feasible region this vector field points inwards, it follows from the Morse inequalities that there is at least one stable equilibrium. When there is a unique, non-stable, interior equilibrium, necessarily the vector field points outwards somewhere along the boundary of the feasible region. This raises to a stable boundary equilibrium. |
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