Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization
We investigate the dynamics of tripodal markets using the response functions, which is a continuation of recent research in the field. Instead of investigating the optimization problem of finding the levels of production that maximize the payoff functions of the participants in an oligopolistic mark...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/171 |
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| author | Aynur Ali Atanas Ilchev Vanya Ivanova Hristina Kulina Polina Yaneva Boyan Zlatanov |
| author_facet | Aynur Ali Atanas Ilchev Vanya Ivanova Hristina Kulina Polina Yaneva Boyan Zlatanov |
| author_sort | Aynur Ali |
| collection | DOAJ |
| description | We investigate the dynamics of tripodal markets using the response functions, which is a continuation of recent research in the field. Instead of investigating the optimization problem of finding the levels of production that maximize the payoff functions of the participants in an oligopolistic market, based on the available statistical data on market presence, we construct a model of the reaction of the participants. This approach allows, in the absence of information about the cost functions of producers and the demand and utility functions of consumers, to construct a model that is statistically reliable and answers the questions about the levels at which the market has reached equilibrium and whether it is sustainable. On the other hand, any external impact, such as changes in the regulations or the behavior of small market participants, is implicitly included in the response functions. The additional analysis confirms that there are no dependencies, even of a nonlinear type, in the constructed models that are not included. Stability and equilibrium are investigated in the proposed models. The statistical performance measurements for the constructed models are calculated, and their credibility is tested. The models demonstrate high statistical performance and adequacy. |
| format | Article |
| id | doaj-art-2c72688e5b9c4f5bbc48d345cb206b63 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2c72688e5b9c4f5bbc48d345cb206b632025-01-10T13:18:30ZengMDPI AGMathematics2227-73902025-01-0113117110.3390/math13010171Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff MaximizationAynur Ali0Atanas Ilchev1Vanya Ivanova2Hristina Kulina3Polina Yaneva4Boyan Zlatanov5Department of Algebra and Geometry, Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 115 Universitetska Str., 9700 Shumen, BulgariaDepartment of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, BulgariaDepartment of Computer Systems, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, BulgariaDepartment of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, BulgariaDepartment of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, BulgariaDepartment of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, BulgariaWe investigate the dynamics of tripodal markets using the response functions, which is a continuation of recent research in the field. Instead of investigating the optimization problem of finding the levels of production that maximize the payoff functions of the participants in an oligopolistic market, based on the available statistical data on market presence, we construct a model of the reaction of the participants. This approach allows, in the absence of information about the cost functions of producers and the demand and utility functions of consumers, to construct a model that is statistically reliable and answers the questions about the levels at which the market has reached equilibrium and whether it is sustainable. On the other hand, any external impact, such as changes in the regulations or the behavior of small market participants, is implicitly included in the response functions. The additional analysis confirms that there are no dependencies, even of a nonlinear type, in the constructed models that are not included. Stability and equilibrium are investigated in the proposed models. The statistical performance measurements for the constructed models are calculated, and their credibility is tested. The models demonstrate high statistical performance and adequacy.https://www.mdpi.com/2227-7390/13/1/171fixed pointtripled fixed pointmarket equilibriumresponse functionsoligopoly market |
| spellingShingle | Aynur Ali Atanas Ilchev Vanya Ivanova Hristina Kulina Polina Yaneva Boyan Zlatanov Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization Mathematics fixed point tripled fixed point market equilibrium response functions oligopoly market |
| title | Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization |
| title_full | Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization |
| title_fullStr | Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization |
| title_full_unstemmed | Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization |
| title_short | Modeling the Tripodal Mobile Market Using Response Functions Instead of Payoff Maximization |
| title_sort | modeling the tripodal mobile market using response functions instead of payoff maximization |
| topic | fixed point tripled fixed point market equilibrium response functions oligopoly market |
| url | https://www.mdpi.com/2227-7390/13/1/171 |
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