A numerical method to solve a duopolistic differential game in a closed-loop equilibrium
| dc.contributor.author | De la Cruz, Jorge H. | |
| dc.contributor.author | Ivorra, Benjamín Pierre Paul | |
| dc.contributor.author | Ramos Del Olmo, Ángel Manuel | |
| dc.date.accessioned | 2023-06-20T09:15:21Z | |
| dc.date.available | 2023-06-20T09:15:21Z | |
| dc.date.issued | 2012-10 | |
| dc.description.abstract | In this work, we develope a numerical method to solve infinite time differential games in closed-loop equilibria. Differential games are thought to be run in dynamic decissions and competitive situations, such as marketing investments and pricing policies in a company. Closed-loop equilibria allow us to obtain strategies as a function of ourselves and our competitor. We apply our algorithm to a real data set of two competitive firms. We show how our algorithm is able to develop a different price-advertising strategy to get bigger benefits | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.status | submitted | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/29056 | |
| dc.identifier.officialurl | http://www.mat.ucm.es/deptos/ma/prepublicaciones/2012/2012-13p.pdf | |
| dc.identifier.relatedurl | http://www.mat.ucm.es/deptos/ma | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49144 | |
| dc.issue.number | 13 | |
| dc.journal.title | Prepublicaciones del Departamento de Matemática Aplicada | |
| dc.language.iso | eng | |
| dc.page.final | 44 | |
| dc.page.initial | 1 | |
| dc.publisher | Universidad Complutense. Departamento de Matemática Aplicada | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 519.6 | |
| dc.subject.cdu | 517.977.8 | |
| dc.subject.keyword | Differential games | |
| dc.subject.keyword | closed-loop equilibrium | |
| dc.subject.keyword | time series models | |
| dc.subject.keyword | Lotka-Volterra models | |
| dc.subject.keyword | Hamilton-Jacobi-Bellman equations | |
| dc.subject.keyword | dynamic programming | |
| dc.subject.ucm | Análisis numérico | |
| dc.subject.ucm | Investigación operativa (Matemáticas) | |
| dc.subject.unesco | 1206 Análisis Numérico | |
| dc.subject.unesco | 1207 Investigación Operativa | |
| dc.title | A numerical method to solve a duopolistic differential game in a closed-loop equilibrium | |
| dc.type | technical report | |
| dcterms.references | 1. Arnason R, Steinsham S, Sandal L, Vestergaard N (2004). Optimal Feedback Controls: Comparative evaluation of the cod fisheries in Denmark,Iceland, and Norway. American Journal of Agricultural Economics.86(2)(May 2004): 531-542. 2. Basar T,Olsder G.J. (1987). Dynamic Non-Cooperative Game Theory. Society for Industrial and Applied Mathematics 3. Cerdo, E. (2000). Optimizacion Dinamica, 1 Edicion. Prentice Hall. 4. Dockner E, Jorgensen S, Van Long N, Sorger G. (2000). Differential games in economics and management science. Cambridge University press. 5. Ewing B.T, R. K. (2006). Time series analysis of a predator-prey system: Application of VAR and generalized impulse response function. Journal of Ecological Economics. 60(Jan 2007): 605-612. 6. Grïene L, Semmpler W. (2004). Using dynamic programming with adaptive grids to solve control problems in economics. Journal of Economic Dynamics and Control. 28(Dec 2004): 2427-2456. 7. Hamilton,J.D. (1994). Time Series Analysis. Princeton University Press. 8. Jorgensen S, Z. G. (2006). Developments in differential game theory and numerical methods:economic and management applications. Journal of Computational Management Science. 4(Apr 2007): 159-181. 9. Kenneth L. Judd, A. S. (2004). Numerical Dynamic Programming with Shape Preserving Splines. Working paper 10. Krishnamoorthy A, P. A. (2010). Optimal pricing and Advertising in a Durable - good duopoly. European Journal of Operational Research, 200(2)(Jan 2010): 486-497. 11. Lopez L, S. M. (2001). Defining strategies to win in the Internet market. Physica A. 301 (jan 2001) 512-534. 12. Manuel S Santos, J. V.-A. (1998). Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models. Econometrica. 66 (2) (1998) 409-426. 13. Michalakelis, C. (2009). Modeling Competition in the Telecommunications Market Based on Concepts of Population Biology. IEEE transactions on systems, man, and cybernetics.41(2) (2011) 200-210. 14. Wan,Q. (1996). A duopolistic model of dynamic Competitive advertising and empirical validation. Nanayang Technological University, Working paper series. 15. Sethi S, Prasad A, He X. (2008). Optimal advertising and pricing in a new product adoption model. Journal of Optimization Theory and Applications.139 (2) (2008)351-360 16. Sigurd, A. (2009). Essais on explotation on natural resources. Optimal control theory applied on multispecies fisheries and fossil fuel extraction. Doctoral Thesis. 17. Stukalin D, Schmidt. W. (2011). Some Applications of Optimal Control in Sustainable Fishing in the Baltic Sea. Applied Mathematics.7(2) (2011) 854-865. 18. Sun, M. (2006). Dynamic Platform Competition in two-sided markets. ProQuest Dissertations and Theses. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 6d5e1204-9b8a-40f4-b149-02d32e0bbed2 | |
| relation.isAuthorOfPublication | 581c3cdf-f1ce-41e0-ac1e-c32b110407b1 | |
| relation.isAuthorOfPublication.latestForDiscovery | 6d5e1204-9b8a-40f4-b149-02d32e0bbed2 |
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