A multilinear interaction model: algorithms for Kalai-Smorodinsky solution
Abstract
We implement Matlab algorithms for the construction and representation of the payoff space in a certain applicable game models, in 2 and 3 dimensions. More- over our algorithms can find the Kalai-Smorodinsky solutions in the same game with some interfering elements. We write down the intersection of the critical zone and the Kalai-Smorodinsky straight-line for finding the compromise solution. We propose a software for the determination of the graphs. In the Appendix we solve the problem in closed form for the 2 and 3 dimensional case and numerical ly for n = 7.
References
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Carfì, D. (2008). Optimal boundaries for decisions. AAPP | Physical, Mathematical, and Natural Sciences 86 (1), 1–11. https://dx.doi.org/10.1478/C1A0801002
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Carfì, D. (2015). A model for coopetitive games. Journal of Mathematical Economics and Finance 1 (1), 46–75. http://journals.aserspublishing.eu/jmef/article/view/585
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Carfì, D. and M. Campbell (2015). Bounded Rational Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets. Journal of Mathematical Economics and Finance 1 (1), 4–28. http://journals.aserspublishing.eu/jmef/article/view/582
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Arthanari, T., D. Carfì, and F. Musolino (2015). Game Theoretic Modeling of Horizontal Supply Chain Coopetition among Growers. International Game Theory Review 17 (2). https://dx.doi.org/10.1142/S0219198915400137
Baglieri, D., D. Carfì, and G. Dagnino (2010). Profiting from Asymmetric R&D Alliances: Coopetitive Games and Firm’s Strategies. Researchgate Paper, 1–48. Presented in 4th Workshop on Coopetition Strategy “Coopetition and Innovation”, Montpellier, France, June 17-18, 2010 (University of Montpellier South of France and GSCM Montpellier Business School). https://dx.doi.org/10.13140/RG.2.1.2072.9043
Baglieri, D., D. Carfì, and G. Dagnino (2012). Asymmetric R&D Alliances and Coopetitive Games. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. Yager (Eds.), Advances in Computational Intelligence, Part IV (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and
Information Science, pp. 607–621. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_64
Baglieri, D., D. Carfi, and G. Dagnino (2015). A Coopetitive Game Model for Asymmetric R&D Alliances within a generalized “Reverse Deal”. In G. Centorrino (Ed.), Economia e Territorio, pp. 15–47. Aracne editrice.
Baglieri, D., D. Carfì, and G. B. Dagnino (2016). Asymmetric R&D Alliances in the Biopharmaceutical Industry. International Studies of Management and Organization 46 (2(3)), 179–201. https://dx.doi.org/10.1080/00208825.2016.1112154
Carfì, D. (2008). Optimal boundaries for decisions. AAPP | Physical, Mathematical, and Natural Sciences 86 (1), 1–11. https://dx.doi.org/10.1478/C1A0801002
Carfì, D. (2009a). Decision-form games. Communications to SIMAI Congress - Proceedings of the 9th Congress of SIMAI, the Italian Society of Industrial and Applied Mathematics, Roma (Italy), September 15-19, 2008 3 (307), 1–12. https://dx.doi.org/10.1685/CSC09307
Carfì, D. (2009b). Differentiable game complete analysis for tourism firm decisions. In Proceedings of the 2009 International Conference on Tourism and Workshop on Sustainable tourism within High Risk areas of environmental crisis, Messina, Italy, April 22-25, 2009, pp. 1–10. University of Messina: SGB. Available as MPRA Paper 29193 at http://mpra.ub.uni-muenchen.de/29193/
Carfì, D. (2009c). Globalization and Differentiable General Sum Games. In Proceedings of the 3rd International Symposium “Globalization and convergence in economic thought”, Bucharest, December 11-12, 2009. Bucaresti: Editura ASE. Available as Researchgate Paper at https://dx.doi.org/10.13140/RG.2.1.2215.8801
Carfì, D. (2009d). Payoff space in C1 Games. Applied Sciences(APPS) 11, 35–47. http://www.mathem.pub.ro/apps/v11/A11-ca.pdf
Carfì, D. (2010a). A model for coopetitive games. MPRA Paper 59633 , 1–25. http://mpra.ub.uni-muenchen.de/59633/
Carfì, D. (2010b). Decision-Form Games. Il Gabbiano. https://dx.doi.org/10.13140/RG.2.1.1320.3927
Carfì, D. (2010c). Foundations of Superposition Theory, vol. 1, Volume 1. Il Gabbiano. https://dx.doi.org/10.13140/RG.2.1.3352.2642
Carfì, D. (2010d). Topics in Game Theory. Il Gabbiano. https://dx.doi.org/10.13140/RG.2.1.4203.9766
Carfì, D. (2012a). Coopetitive games and applications. In R. Mishra, S. Deman, M. Salunkhe, S. Rao, and J. Raveendran (Eds.), Advances and Applications in Game Theory - International Conference in honor of prof. Rao, pp. 128–147. J. Macmillan, India. Available as Researchgate Paper at https://dx.doi.org/10.13140/RG.2.1.3526.6005
Carfì, D. (2012b). Fondamenti di Teoria delle Decisioni, volume 1 - Teoria dei preordini e applicazioni. (Foundations of Decision Theory, vol. 1 - Theory of preorders and applications). Antipodes. http://www.antipodes.it/prodotti/scheda-prodotto.asp?id=23
Carfì, D. (2015). A model for coopetitive games. Journal of Mathematical Economics and Finance 1 (1), 46–75. http://journals.aserspublishing.eu/jmef/article/view/585
Carfì, D. (2017). A game Pareto complete analysis in n-dimensions: a general applicative study case. Journal of Mathematical Economics and Finance. In print in Summer Issue.
Carfì, D. and M. Campbell (2015). Bounded Rational Speculative and Hedging Interaction Model in Oil and U.S. Dollar Markets. Journal of Mathematical Economics and Finance 1 (1), 4–28. http://journals.aserspublishing.eu/jmef/article/view/582
Carfì, D., M. Campbell, and A. Donato (2016). Partial selling in a coopetitive Alliance within Pharmaceutical industry: a complete study case. In G. Centorrino (Ed.), Economia e Territorio: prospettive di analisi. Aracne editrice.
Carfì, D. and A. Donato (2016a). A critical analytic survey of an Asymmetric R&D Alliance in Pharmaceutical industry: bi-parametric study case. Journal of Mathematical Economics and Finance 2 (1(2)), 21–57. http://journals.aserspublishing.eu/jmef/article/view/587
Carfì, D. and A. Donato (2016b). Complete study of a coopetitive R&D Alliance. Journal of Mathematical Economics and Finance 2 (2(3)), 35–66. http://journals.aserspublishing.eu/jmef/article/view/922
Carfì, D., A. Donato, and G. Gambarelli (2017). Kalai-Smorodinsky Balance for n-tuples of Interfering Elements. LNCS Transaction on Computational Collective Intelligence. In print.
Carfì, D., A. Donato, and D. Panuccio (2017). A Game Theory Coopetitive Perspective for Sustainability of Global Feeding: Agreements Among Vegan and Non-Vegan Food Firms. In A. J. Vasile and D. Nicoló (Eds.), Sustainable Entrepreneurship and Investments in the Green Economy, Book Series on Advances in Business Strategy and Competitive Advantage (ABSCA), pp. 100–143. IGI Global. https://dx.doi.org/10.4018/978-1-5225-2075-7.ch004
Carfì, D. and C. Fici (2012). The government-taxpayer game. Theoretical and Practical Research in Economic Fields 3 (1(5)), 13–25. http://journals. aserspublishing.eu/tpref/article/view/1166
Carfì, D. and G. Gambarelli (2015). Balancing Bilinearly Interfering Elements. Decision Making in Manufacturing and Services 9 (1), 27–49. http://dx.doi.org/10.7494/dmms.2015.9.1.27 ;
https://journals.agh.edu.pl/dmms/article/view/1676/1410
Carfì, D., G. Gambarelli, and A. Uristani (2013). Balancing pairs of interfering elements. Zeszyty Naukowe Uniwersytetu Szczeci`nskiego - Finanse, Rynki Finansowe, Ubezpieczenia 760 (59), 435–442. Available as Researchgate Paper at http://www.researchgate.net/publication/259323035_Balancing_pairs_of_interfering_elements
Carfì, D. and F. Lanzafame (2013). A Quantitative Model of Speculative Attack: Game Complete Analysis and Possible Normative Defenses. In M. Bahmani-Oskooee and S. Bahmani (Eds.), Financial Markets: Recent Developments, Emerging Practices and Future Prospects, Chapter 9. Nova Science. https://www.novapublishers.com/catalog/product_info.php?products_id=46483
Carfì, D. and M. Magaudda (2009). Complete study of linear infinite games. Proceedings of the International Geometry Center - International Conference “Geometry in Odessa 2009”, 25-30 May 2009, Odessa, Ukraine 2 (3), 19–30. Available as Researchgate Paper at https://www.researchgate.net/publication/283048363_Complete_study_of_linear_infinite_games
Carfì, D., M. Magaudda, and D. Schilirò (2010). Coopetitive game solutions for the eurozone economy. In Quaderni di Economia ed Analisi del Territorio, Quaderno n. 55/2010, pp. 1–21. Il Gabbiano. Available as MPRA Paper at http://mpra.ub.uni-muenchen.de/26541/
Carfì, D. and F. Musolino (2011a). Fair Redistribution in Financial Markets: a Game Theory Complete Analysis. Journal of Advanced Studies in Finance 2 (2(4)), 74–100. http://journals.aserspublishing.eu/jasf/article/view/47
Carfì, D. and F. Musolino (2011b). Game complete analysis for financial markets stabilization. In R. Mirdala (Ed.), Proceedings of the first international on-line conference on ‘Global Trends in Finance’, pp. 14–42. ASERS Publishing House. http://www.asers.eu/asers_files/conferences/GTF/GTF_eProceedings_last.pdf
Carfì, D. and F. Musolino (2012a). A Coopetitive Approach to Financial Markets Stabilization and Risk Management. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. Yager (Eds.), Advances in Computational Intelligence, Part IV (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and Information Science, pp. 578–592. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_62
Carfì, D. and F. Musolino (2012b). A game theory model for currency markets stabilization. MPRA Paper 39240 , 1–38. http://mpra.ub.uni-muenchen.de/39240/
Carfì, D. and F. Musolino (2012c). Game theory and speculation on government bonds. Economic Modelling 29 (6), 2417–2426. https://dx.doi.org/10.1016/j.econmod.2012.06.037
Carfì, D. and F. Musolino (2012d). Game theory model for European government bonds market stabilization: a saving-State proposal. MPRA Paper 39742 , 1–27. http://mpra.ub.uni-muenchen.de/39742/
Carfì, D. and F. Musolino (2012e). Game Theory Models for Derivative Contracts: Financial Markets Stabilization and Credit Crunch, Complete Analysis and Coopetitive Solution. Lambert Academic Publishing. https://www.lap-publishing.com/catalog/details//store/gb/book/978-3-659-13050-2/game-theory-models-for-derivative-contracts
Carfì, D. and F. Musolino (2013a). Credit Crunch in the Euro Area: A Coopetitive Multi-agent Solution. In A. G. S. Ventre, A. Maturo, u. Ho˘skovà-Mayerovà, and J. Kacprzyk (Eds.), Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences, Volume 305 of Studies in Fuzziness and Soft Computing, pp. 27–48. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-35635-3_3
Carfì, D. and F. Musolino (2013b). Game theory application of Monti’s proposal for European government bonds stabilization. Applied Sciences 15, 43–70. http://www.mathem.pub.ro/apps/v15/A15-ca.pdf
Carfì, D. and F. Musolino (2013c). Model of Possible Cooperation in Financial Markets in presence of tax on Speculative Transactions. AAPP | Physical, Mathematical, and Natural Sciences 91 (1), 1–26. https://dx.doi.org/10.1478/AAPP.911A3
Carfì, D. and F. Musolino (2014a). Dynamical Stabilization of Currency Market with Fractal-like Trajectories. Scientific Bulletin of the Politehnica University of Bucharest 76 (4), 115–126. http://www.scientificbulletin.upb.ro/rev_docs_arhiva/rezc3a_239636.pdf
Carfì, D. and F. Musolino (2014b). Speculative and hedging interaction model in oil and U.S. dollar markets with financial transaction taxes. Economic Modelling 37 (0), 306–319. https://dx.doi.org/10.1016/j.econmod.2013.11.003
Carfì, D. and F. Musolino (2015a). A coopetitive-dynamical game model for currency markets stabilization. AAPP | Physical, Mathematical, and Natural Sciences 93 (1), 1–29. https://dx.doi.org/10.1478/AAPP.931C1
Carfì, D. and F. Musolino (2015b). Tax Evasion: A Game Countermeasure. AAPP | Physical, Mathematical, and Natural Sciences 93 (1), 1–17. https://dx.doi.org/10.1478/AAPP.931C2
Carfì, D., G. Patanè, and S. Pellegrino (2011). Coopetitive games and sustainability in Project Financing. In Moving from the crisis to sustainability. Emerging issues in the international context, pp. 175–182. Franco Angeli. http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?CodiceLibro=365.906
Carfì, D. and E. Perrone (2011a). Asymmetric Bertrand Duopoly: Game Complete Analysis by Algebra System Maxima. In L. Ungureanu (Ed.), Mathematical Models in Economics, pp. 44–66. ASERS Publishing House. http://www.asers.eu/asers-publishing/collections.html
Carfì, D. and E. Perrone (2011b). Game Complete Analysis of Bertrand Duopoly. Theoretical and Practical Research in Economic Fields 2 (1(3)), 5–22. http://www.asers.eu/journals/tpref/tpref-past-issues.html
Carfì, D. and E. Perrone (2011c). Game Complete Analysis of Bertrand Duopoly. In L. Ungureanu (Ed.), Mathematical Models in Economics, pp. 22–43. ASERS Publishing House. http://www.asers.eu/estore/books/mathematical-models-in-economics-chapter-1-915.html
Carfì, D. and E. Perrone (2012). Game Complete Analysis of Classic Economic Duopolies. Lambert Academic Publishing. https://www.lap-publishing.com/catalog/details//store/ru/book/978-3-8484-2099-5/game-complete-analysis-of-classic-economic-duopolies
Carfì, D. and E. Perrone (2013). Asymmetric Cournot Duopoly: A Game Complete Analysis. Journal of Reviews on Global Economics 2, 194–202. https://dx.doi.org/10.6000/1929-7092.2013.02.16
Carfì, D. and A. Pintaudi (2012). Optimal Participation in Illegitimate Market Activities: Complete Analysis of 2-Dimensional Cases. Journal of Advanced Research in Law and Economics 3 (1(5)), 10–25. http://journals. aserspublishing.eu/jarle/article/view/855
Carfì, D. and A. Ricciardello (2009). Non-reactive strategies in decision-form games.
AAPP | Physical, Mathematical, and Natural Sciences 87 (2), 1–12. https://dx.doi.org/10.1478/C1A0902002
Carfì, D. and A. Ricciardello (2010). An algorithm for payoff space in C1-Games. AAPP | Physical, Mathematical, and Natural Sciences 88 (1), 1–19. https://dx.doi.org/10.1478/C1A1001003
Carfì, D. and A. Ricciardello (2011). Topics in Game Theory. Il Gabbiano. https://dx.doi.org/10.13140/RG.2.1.2368.9685
Carfì, D. and A. Ricciardello (2012a). Algorithms for Payoff Trajectories in C1 Parametric Games. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. R. Yager (Eds.), Advances in Computational Intelligence (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and Information Science, pp. 642–654. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_67
Carfì, D. and A. Ricciardello (2012b). Topics in Game Theory. Applied Sciences - Monographs 9, Balkan Society of Geometers. http://www.mathem.pub.ro/apps/mono/A-09-Car.pdf
Carfì, D. and A. Ricciardello (2013a). An Algorithm for Dynamical Games with Fractal-Like Trajectories. In D. Carfì, M. Lapidus, E. Pearse, and M. Van Frankenhuijsen (Eds.), Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics. (PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, Messina, Italy, November 8-12, 2011 - AMS Special Session on Fractal Geometry in Pure and Applied Mathematics: in memory of Benoît Mandelbrot, Boston, Massachusetts, January 4-7, 2012 - AMS Special Session on Geometry and Analysis on Fractal Spaces, Honolulu, Hawaii, March 3-4, 2012), Volume 601 of Contemporary Mathematics, pp. 95–112. American Mathematical Society. https://dx.doi.org/10.1090/conm/601/11961
Carfì, D. and A. Ricciardello (2013b). Computational representation of payoff scenarios in C1-families of normal-form games. Uzbek Mathematical Journal 1, 38–52. Available as Researchgate Paper at https://www.researchgate.net/publication/259105575_Computational_representation_of_payoff_scenarios_in_C1-families_of_normal-form_games
Carfì, D. and A. Romeo (2015). Improving Welfare in Congo: Italian National Hydrocarbons Authority Strategies and its Possible Coopetitive Alliances with Green Energy Producers. Journal of Applied Economic Sciences 10 (4 (34)), 571–592. http://cesmaa.eu/journals/jaes/files/JAES_summer%204(34)_online.pdf
Carfì, D. and D. Schilirò (2011a). Coopetitive games and global Green Economy. In Moving from the Crisis to Sustainability. Emerging Issues in the International Context, pp. 357–366. Franco Angeli. http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?CodiceLibro=365.906
Carfì, D. and D. Schilirò (2011b). Crisis in the Euro Area: Co-opetitive Game Solutions as New Policy Tools. In L. Ungureanu (Ed.), Mathematical Models in Economics, pp. 67–86. ASERS Publishing House. http://www.asers.eu/asers-publishing/collections.html
Carfì, D. and D. Schilirò (2011c). Crisis in the Euro Area. Coopetitive Game Solutions as New Policy Tools. Theoretical and Practical Research in Economic Fields 2 (1(3)), 23–36. http://journals.aserspublishing. eu/tpref/article/view/1109
Carfì, D. and D. Schilirò (2012a). A Framework of coopetitive games: Applications to the Greek crisis. AAPP | Physical, Mathematical, and Natural Sciences 90 (1), 1–32. https://dx.doi.org/10.1478/AAPP.901A1
Carfì, D. and D. Schilirò (2012b). A Model of Coopetitive Game for the Environmental Sustainability of a Global Green Economy. Journal of Environmental Management and Tourism 3 (1(5)), 5–17. http://journals.aserspublishing.eu/jemt/article/view/378
Carfì, D. and D. Schilirò (2012c). A coopetitive model for the green economy. Economic Modelling 29 (4), 1215–1219. https://dx.doi.org/10.1016/j.econmod.2012.04.005
Carfì, D. and D. Schilirò (2012d). Global Green Economy and Environmental Sustainability: A Coopetitive Model. In S. Greco, B. Bouchon-Meunier, G. Coletti, M. Fedrizzi, B. Matarazzo, and R. Yager (Eds.), Advances in Computational Intelligence (14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV), Volume 300 of Communications in Computer and Information Science, pp. 593–606. Springer Berlin Heidelberg. https://dx.doi.org/10.1007/978-3-642-31724-8_63
Carfì, D. and D. Schilirò (2013). A Model of Coopetitive Games and the Greek Crisis. In L. Petrosyan and N. Zenkevich (Eds.), Contributions to Game Theory and Management, Volume 6, pp. 35–62. Saint Petersburg State University. Collected papers presented on the Sixth International Conference Game Theory and Management, St. Petersburg, Russia, June 27-29, 2012. http://www.gsom.spbu.ru/files/upload/gtm/sbornik2012_27_05_2013.pdf
Carfì, D. and D. Schilirò (2014a). Coopetitive Game Solutions for the Greek Crisis. In D. Schilirò (Ed.), Design a Pattern of Sustainable Growth. Innovation, Education, Energy and Environment. ASERS Publishing House. http://books.aserspublishing.eu/eoconomica/catalog/book/2
Carfì, D. and D. Schilirò (2014b). Improving Competitiveness and Trade Balance Of Greek Economy: A Coopetitive Strategy Model. Journal of Applied Economic Sciences 9 (2(28)), 211–220. http://www.ceeol.com/aspx/issuedetails.aspx?issueid=583d6083-2bbf-4d8c-af1f-3b5786c6e087&articleId=8c9be4cb-86d9-43f1-b555-58b8cb28bbeb
Carfì, D. and A. Trunfio (2011). A non-linear coopetitive game for global Green Economy. In Moving from the Crisis to Sustainability - Emerging Issues in the International Context, pp. 421–428. Franco Angeli. http://www.francoangeli.it/Ricerca/Scheda_libro.aspx?CodiceLibro=365.906
Okura, M. and D. Carfì (2014). Coopetition and Game Theory. Journal of Applied Economic Sciences 9 (3(29)), 458–469. http://cesmaa.eu/journals/jaes/files/JAES_2014_Fall.pdf#page=123
Published
2017-08-25
How to Cite
DONATO, Alessia.
A multilinear interaction model: algorithms for Kalai-Smorodinsky solution.
Journal of Mathematical Economics and Finance, [S.l.], v. 3, n. 1, p. 47 - 76, aug. 2017.
ISSN 2458-0813.
Available at: <https://journals.aserspublishing.eu/jmef/article/view/1355>. Date accessed: 22 dec. 2024.
doi: https://doi.org/10.14505//jmef.v3.1(4).03.
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