Abstract
Game theory is a mathematical framework for strategy analysis and design as well as for optimal decision-making under conflict and behavioral uncertainty. On the one hand, game theory plays a key role for modern economics; on the other, it suggests possible approaches and solutions for complex strategic problems in various fields of human activity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Originates from The Bible, Acts 20:35: “In all things I have shown you that by working hard in this way we must help the weak and remember the words of the Lord Jesus, how he himself said, ‘It is more blessed to give than to receive.”’
- 2.
Give equal shares to all. Daniel Defoe appears to be the first to have used this phrase in The Life and Strange Adventures of Robinson Crusoe (1719): “He declar’d he had reserv’d nothing from the Men, and went Share and Share alike with them in every Bit they eat.”
- 3.
People should accept the way other people live and behave, especially if they do things in a different way.
- 4.
A fragment from Ruslan and Lyudmila, a poem by Aleksandr S. Pushkin, (1799–1837), a Russian poet, novelist, dramatist, and short-story writer. Considered as the greatest poet and founder of modern Russian literature.
References
Gorelik, V.A., Gorelov, M.A., and Kononenko, A.F., Analiz konfliktnykh situatsii v sistemakh upravleniya (Analysis of Conflict Situations in Control Systems), Moscow: Radio i Svyaz’, 1991.
Zhukovskiy, V.I., Smirnova, L.V., and Gorbatov, A.S., Mathematical Foundations of the Golden Rule. II. Dynamic Case, Mat. Teor. Igr Prilozh., 2016, vol. 8, no. 1, pp. 27–62.
Zhukovskiy, V.I. and Salukvadze, M.E., Mnogoshagovye pozitsionnye konflikty i ikh prilozheniya (Multistage Positional Conflicts and Their Applications), Moscow–Tbilisi: Intelekti, 2011.
Zhukovskiy, V.I. and Salukvadze, M.E., Nekotorye igrovye zadachi upravleniya i ikh prilozheniya (Some Game-Theoretic Problems of Control and Their Applications), Tbilisi: Metsniereba, 1998.
Kudryavtsev, K.N., Coordinated Solutions in Multiagent Information Environment, Extended Abstract of Cand. Sci. Dissertation (Phys.-Math.), South-Ural Fed. Univ., Chelyabinsk, 2011.
Kudryavtsev, K.N. and Stabulit, I.S., Strongly-Guaranteed Equilibrium in One Spatial Competition Problem, Tr. XVI Mezhd. Konf. “Sistemy komp’yuternoy matematiki i ikh prilozheniya” (Proc. XVI Int. Conf. “Systems of Computer Mathematics and Their Applications”), Smolensk: Gos. Univ., 2015, vol. 16, pp. 181–183.
Lavrov, P.L., Sotsial’naya revolyutsiya i zadachi nravstvennosti. Tom 1 (Social Revolution and Ethical Tasks. Vol. 1), Moscow: Mysl’, 1965.
Malkin, I.G., Teoriya ustoychivosti dvizheniya (Theory of Motion Stability), Moscow: Nauka, 1996.
Muschick, E. and Müller, P., Metody prinyatiya tekhnicheskikh reshenii (Methods of Technical Decision-Making), Moscow: Mir, 1990.
Pecherskii, S.L. and Belyaeva, A.A., Teoriya igr dlya ekonomistov. Vvodnyy kurs (Game Theory for Economists. An Introductory Course), St. Petersburg: Evrop. Univ., 2004.
Pisarchuk, N.N., Vvedenie v teoriyu igr (Introduction to Game Theory), Minsk: Belorus. Gos. Univ., 2011.
Podinovskii, V.V., General Zero-Sum Two-Person Games, Zh. Vychisl. Mat. Matem. Fiz., 1981, vol. 21, no. 5, pp. 1140–1153.
Podinovskii, V.V., The Principle of Guaranteed Result for Partial Preference Relations, Zh. Vychisl. Mat. Matem. Fiz., 1979, vol. 19, no. 6, pp. 1436–1450.
Podinovskii, V.V. and Noghin, V.D., Pareto-optimal’nye resheniya mnogokriterial’nykh zadach (Pareto Optimal Solutions of Multicriteria Problems), Moscow: Fizmatlit, 2007.
Russko–anglo–nemetskii tolkovyi slovar’ po biznesu (Russian–English–German Glossary on Business Science), Kuznetsova, N.N., Novikova, E.V., Plekhanov, S.V., and Chekmezov, N.A., Eds., Moscow: Gorizont, 1992.
Smol’yakov, E.R., Teoriya konfliktnykh ravnovesii (Theory of Conflict Equilibria), Moscow: URSS, 2004.
Fischer, S., Dornbusch, R., and Schmalensee, R., Economics, McGraw-Hill, 1988.
Shubik, M., The Present and Past of Game Theory, Mat. Teor. Igr Prilozh., 2012, vol. 4, no. 1, pp. 93–116.
Entsiklopediya matematiki. Tom 1–5. (Encyclopeadia of Mathematics. Vols. 1–5), Moscow: Sovetsk. Entsiklop., 1977–1985.
A century of mathematics in America 1988–1989, vol. 1–3, ed. AMS (vol. 1. P. 382).
Archibald, R.C., A Semicentennial History of American Mathematical Society. 1888–1938 (2 vols.), 1938.
Berge, C., Théorie générale des jeux ánpersonnes games, Paris: Gauthier Villars, 1957. (Russian translation: Berge, C., Obshchaya teoriya igr neskol’kikh lits, Moscow: Fizmatgiz, 1961).
Bertrand, J., Caleul des probabilities, Paris, 1888.
Bertrand, J., Book review of theorie mathematique de la richesse sociale and of recherches sur les principles mathematiques de la theorie des richesses, Journal de Savants, 1883, vol. 67, pp. 499–508.
Borel, E., Sur les systemes de formes lineares a determinant symetrique gauche et la theorie generale du jeu, Comptes Rendus de l’Academie des Sciences, 1927, vol. 184, pp. 52–53.
Cournot, A., Principes de la theorie des richeses, Paris, 1863.
Cournot, A., Recherches sur les principes mathématiques de la théorie de richesses, Paris, 1838.
Geoffrion, A.M., Proper Efficiency and the Theory of Vector Maximization, J. Math. Anal. and Appl., 1968, vol. 22, no. 3, pp. 618–630.
Lung, R.I., Gaskó, N., and Dumitrescu, D., Characterization and Detection of 𝜖-Berge-Zhukovskii Equilibria, PLoS ONE, 2015, vol. 10, no. 7: e0131983. DOI:10.1371/journal.pone.0131983
Van Megen, F., Born, P., and Tijs, S., A Preference Concept for Multicriteria Game, Mathematical Methods of OR, 1999, vol. 49, no. 3, pp. 401–412.
Nash, J.F., Non-Cooperative Games, Ann. Math., 1951, vol. 54, pp. 286–295.
Nash, J.F., Equilibrium Points in N-Person Games, Proc. Nat. Academ. Sci. USA, 1950, vol. 36, pp. 48–49.
Nessah, R., Larbani, M., and Tazdait, T., A Note on Berge Equilibrium, Applied Mathematics Letters, 2007, vol. 20, no. 8, pp. 926–932.
Von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behavior, Princeton Univ. Press, 1944.
Pottier, A. and Nessah, R., Berge-Vaisman and Nash Equilibria: Transformation of Games, International Game Theory Review, 2014, vol. 16, no. 4, p. 1450009.
Shubik, M., Review of C. Berge “General theory of n-person games,” Econometrica, 1961, vol. 29, no. 4, p. 821.
Steuer, R., Multiple Criteria Optimization: Theory, Computation and Application, New York: John Wiley and Sons, 1986.
Tanaka, T., Two Types of Minimax Theorems for Vector-Valued Functions, J. Optimiz. Theory and Appl., 1991, vol. 68, no. 2, pp. 321–334.
Vaisbord, E.M. and Zhukovskiy, V.I., Introduction to Multi Player Differential Games and Their Applications, New York: Gordon and Breach, 1988.
Wald, A., Statistical Decision Functions, New York: Wiley, 1950.
Zhukovskiy, V.I., Lyapunov Functions in Differential Games, London and New York: Taylor and Francis, 2003.
Zhukovskiy, V.I. and Larbani, M., Alliance in Three Person Games, Dostizhen. Matem. Mekhan., 2017, vol. 22, no. 1 (29), pp. 105–119.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
E. Salukvadze, M., I. Zhukovskiy, V. (2020). Conclusion. In: The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25546-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-25546-6_6
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-25545-9
Online ISBN: 978-3-030-25546-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)