Complex dynamics and multistability with increasing rationality in market games |
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| Affiliation: | 1. Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell’Ateneo Nuovo 1, 20126 Milano, Italy;2. Department of Mathematical Sciences, Mathematical Finance and Econometrics, Catholic University of the Sacred Heart, Via Necchi 9, 20123 Milano, Italy;1. Centro Brasileiro de Pesquisas Físicas, Rua Dr Xavier Sigaud 150, 22290-180 Urca, Rio de Janeiro, RJ, Brazil;2. Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro, RJ, Brazil;1. Sobell Department of Motor Neuroscience and Movement Disorders, The National Hospital of Neurology and Neurosurgery, Institute of Neurology, University College London, London, United Kingdom;2. International Parkinson''s Centre of Excellence, King''s College and King''s College Hospital, Denmark Hill Campus, London, United Kingdom;3. Queen Elizabeth Hospital, Woolwich, Lewisham & Greenwich NHS Trust, London, United Kingdom;4. Department of Neuropsychiatry, BSMHFT and University of Birmingham, United Kingdom;5. Section of Child Neuropsichiatry, Dipartimento di Scienze Mediche e Pediatriche, Catania University, Catania, Italy;6. Centre de Référence National Maladie Rare: Syndrome Gilles de la Tourette, Département de Neurologie, Pôle des Maladies du Système Nerveux, France;7. Department of Child and Adolescent Psychiatry, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands;8. TANDeM Clinic-Evelina London Children''s Hospital at Guys and St. Thomas'', Kings Health Partners AHSC, London, United Kingdom;9. Pediatric Department, Glostrup University Hospital, Glostrup, Denmark;10. Clinic of Psychiatry, Socialpsychiatry and Psychotherapy, Hannover Medical School, Carl-Neuberg-Street 1, D-30625 Hannover, Germany;11. Institute of Neuroscience and Medicine 4, (INM 4), Forschungszentrum, Jülich, Jülich, Germany;12. Department of Psychiatry, Psychotherapy and Psychosomatics, RWTH Aachen University, JARA-BRAIN — Translational Medicine, Germany;13. Departments of Neurosurgery and Neurology, IRCCS Galeazzi, Milan, Italy;14. Department of Psychology, University of Rome, La Sapienza, Rome, Italy;15. Klinik und Poliklinikfür Kinder- und Jugendpsychiatrie und -psychotherapie, TechnischeUniversität Dresden, Germany |
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| Abstract: | In this work we study oligopoly models in which firms adopt decision mechanisms based on best response techniques with different rationality degrees. Firms are also assumed to face resource or financial constraints in adjusting their production levels, so that, from time to time, they can only increase or decrease their strategy by a bounded quantity. We consider different families of oligopolies of generic sizes, characterized by heterogeneous compositions with respect to the rationality degrees of firms. We analytically study the local stability of the equilibrium depending on the oligopoly size and composition and through numerical simulations we investigate the possible dynamics arising when trajectories do not converge toward the equilibrium. We show that in this case complex dynamics can arise, and this is due to both the loss of stability of the equilibrium and to the emergence of multiple attractors, with the stable steady state coexisting with a different, periodic or chaotic, attractor. In particular, we show that multistability phenomena occur when the overall degree of rationality of the oligopoly is increased. Finally, we investigate the effect of non-convergent dynamics on the realized profits. |
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