Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities
The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is n...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/6885051 |
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| author | R. Israel Ortega-Gutiérrez Raúl Montes-de-Oca Hugo Cruz-Suárez |
| author_facet | R. Israel Ortega-Gutiérrez Raúl Montes-de-Oca Hugo Cruz-Suárez |
| author_sort | R. Israel Ortega-Gutiérrez |
| collection | DOAJ |
| description | The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the α-cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model. |
| format | Article |
| id | doaj-art-6cc86d73f0594392a415f5ab1901428d |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6cc86d73f0594392a415f5ab1901428d2025-02-03T01:32:20ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/6885051Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy UtilitiesR. Israel Ortega-Gutiérrez0Raúl Montes-de-Oca1Hugo Cruz-Suárez2Faculty of Mathematical Physical SciencesMathematics DepartmentFaculty of Mathematical Physical SciencesThe article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the α-cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model.http://dx.doi.org/10.1155/2024/6885051 |
| spellingShingle | R. Israel Ortega-Gutiérrez Raúl Montes-de-Oca Hugo Cruz-Suárez Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities Journal of Mathematics |
| title | Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities |
| title_full | Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities |
| title_fullStr | Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities |
| title_full_unstemmed | Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities |
| title_short | Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities |
| title_sort | characterization of a cournot nash equilibrium for a fishery model with fuzzy utilities |
| url | http://dx.doi.org/10.1155/2024/6885051 |
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