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The Berge Equilibrium: a Game-Theoretic Framework for the Golden Rule of Ethics

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The Berge Equilibrium: a Game-Theoretic Framework for the Golden Rule of Ethics Static & Dynamic Game Theory: Foundations & Applications Mindia E. Salukvadze Vladislav I. Zhukovskiy The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics Static & Dynamic Game Theory: Foundations & Applications Series Editor Tamer Ba¸sar, University of Illinois, Urbana-Champaign, IL, USA Editorial Advisory Board Daron Acemoglu, MIT, Cambridge, MA, USA Pierre Bernhard, INRIA, Sophia-Antipolis, France Maurizio Falcone , Università degli Studi di Roma “La Sapienza,” Italy Alexander Kurzhanski, University of California, Berkeley, CA, USA Ariel Rubinstein, Tel Aviv University, Ramat Aviv, Israel; New York University, NY, USA William H. Sandholm, University of Wisconsin, Madison,WI, USA Yoav Shoham, Stanford University, CA, USA Georges Zaccour, GERAD, HEC Montréal, Canada More information about this series at http://www.springer.com/series/10200 Mindia E. Salukvadze • Vladislav I. Zhukovskiy The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics Mindia E. Salukvadze Vladislav I. Zhukovskiy Department of Engineering Sciences and Department of Optimal Control Information Technology Faculty of Computational Mathematics Georgian National Academy of Sciences and Cybernetics Tbilisi, Georgia Moscow State University Moscow, Russia ISSN 2363-8516 ISSN 2363-8524 (electronic) Static & Dynamic Game Theory: Foundations & Applications ISBN 978-3-030-25545-9 ISBN 978-3-030-25546-6 (eBook) https://doi.org/10.1007/978-3-030-25546-6 Mathematics Subject Classification (2010): 49-XX, 49N70, 49N90, 90-XX, 90C47, 90B50, 91-XX, 91A10, 91A23, 91A80, 91Bxx, 91B06, 91B30 © Springer Nature Switzerland AG 2016, 2020 Original Russian edition published by Georgian National Academy of Sciences, Tbilisi, Georgia, 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Mindia E. Salukvadze (May 3, 1933–December 27, 2018) Dedicated to the memory of Mindia E. Salukvadze. Biography of Mindia E. Salukvadze A man is measured by his deeds and contribution to the global pool of values. This is an axiom. Just listing all the academic degrees, posts and titles of Mindia E. Salukvadze forms the picture of an extraordinary personality. Mindia E. Salukvadze was born in 1933 in Tbilisi, and grew up as an orphan. His parents were subjected to repression in 1937 (subsequently both were fully exonerated). In 1955, he received Diploma with honors from the Physics Faculty of Tbilisi State University. His postgraduate studies were continued at the Institute of Electronics, Automation and Remote Control of the USSR Academy of Sciences (presently, Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences), where he defended first the Candidate’s Dissertation (1963) and then the Doctor’s Dissertation (1974) in Engineering. In 1983, Mindia E. Salukvadze was elected a Corresponding Member of the Academy of Sciences of the Georgian SSR; in 1993, a Full Member of the Georgian National Academy of Sciences. Later on, he became the Academician-secretary of the Department for Applied Mechanics, Machine Building, Energy and Control Processes of the Academy and also a Member of the Academy’s Presidium. In 1996, he was awarded the Nikoladze Prize of the Academy, which was established as back as 1973 for the best scientific works in engineering. In 1996 and again in 2004, he was awarded the State Prize of Georgia in the field of science and technology. In 2014, he and Vladislav I. Zhukovskiy became the winners of the International Contest for the Best Scientific Book, held in Russia. For many years, Mindia E. Salukvadze was the Head of the Georgian Section of the International Federation of Automatic Control (IFAC) as well as a member of the editorial boards of several scientific journals such as Moambe (Bulletin of the Georgian National Academy of Sciences), International Journal of Infor- mation Technology and Decision Making,andAutomation and Remote Control (Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences). In addition, he was a member of several scientific councils and organizations. Mindia E. Salukvadze had close cooperation with a series of research centers all over the world and participated in leading international conferences and symposia. He was ix x Biography of Mindia E. Salukvadze a member of different international academies of sciences, including the New York Academy of Sciences (since 1994). For 25 years, Academician Mindia E. Salukvadze was Director of the Eliashvili Institute of Control Systems (1981–2006), and then Chairman of the Institute’s Scientific Council. The research interests of Mindia E. Salukvadze covered the stability of control systems and the theory of optimal control. He authored over 140 scientific papers, 13 monographs and 6 textbooks, known in Georgia and also abroad. Salukvadze’s method, Salukvadze’s solution, Salukvadze’s principle—these terms were intro- duced by American and Russian researchers. In 1975, Metsniereba Press (Tbilisi) published Mindia E. Salukvadze’s well known monograph Zadachi vektornoi optimizatsii v teorii upravleniya,whichwas translated into English under the title Vector-Valued Optimization Problems in Control Theory and published by Academic Press in 1979. Another prominent monograph by Mindia E. Salukvadze, Vector-Valued Maximin (in co-authorship with Vladislav I. Zhukovskiy), was published by Academic Press in 1994. Mindia E. Salukvadze was a fruitful educator, holding the position of Professor at Tbilisi State University. He supervised a series of Doctor’s and Candidate’s Dissertations. The major books by Mindia E. Salukvadze are as follows. 6 Textbooks 1. Gugushvili, A., Salukvadze, M., and Chichinadze, V., Optimal and Adaptive Systems. Book I. Static Optimization, Tbilisi: Teknikuri Universiteti, 1997, 290 p. (in Georgian). 2. Gugushvili, A., Salukvadze, M., Chichinadze, V., Optimal and Adaptive Systems. Book II. Optimal Control of Dynamic Systems, Tbilisi: Teknikuri Universiteti, 1997, 437 p. (in Georgian). 3. Gugushvili, A., Salukvadze, M., Chichinadze, V., Optimal and Adaptive Systems. Book III. Optimal Control of Stochastic Systems. Adaptive Control of Systems, Tbilisi: Teknikuri Universiteti, 1997, 325 p. (in Georgian). 4. Gugushvili, A., Topchishvili, A., Salukvadze, M., Chichinadze, V., and Jabladze, N., Optimization Methods, Tbilisi: Teknikuri Universiteti, 2002, 634 p. (in Georgian). 5. Zhukovskiy, V.I. and Salukvadze, M.E., Otsenka riskov i garantii v konfliktakh (Estimation of Risks and Guarantees in Conflicts), Moscow: Yurait, 2018, 302 p. (in Russian). 6. Zhukovskiy, V.I. and Salukvadze, M.E., Otsenka riskov i mnogoshagovye poz- itsionnye konflikty (Estimation of Risks and Multistage Positional Conflicts), Moscow: Yurait, 2018, 306 p. (in Russian). 13 Monographs 1. Salukvadze, M.E., Zadachi vektornoi optimizatsii v teorii upravleniya (Vector- Valued Optimization Problems in Control Theory), Tbilisi: Metsniereba, 1975, 201 p. (in Russian). Biography of Mindia E. Salukvadze xi 2. Salukvadze, M.E., Vector-Valued Optimization Problems in Control Theory, New York: Academic Press, 1979, 219 p. 3. Ioseliani, A.N., Mikhalevich, A.A., Nesterenko V.V., and Salukvadze, M.E., Metody optimizatsii parametrov teploobmennykh apparatov AES (Parameter Optimization Methods for the Heat-Exchange Systems of Nuclear Power Plants), Minsk: Nauka i Tekhnika, 1981, 144 p. (in Russian). 4. Salukvadze, M.E., Zadacha A.M. Letova o sinteze optimal’nykh sistem avtomaticheskogo upravleniya (A.M. Letov’s Problem on Optimal Automatic Control Systems Design), Tbilisi: Metsniereba, 1988. 381 p. (in Russian). 5. Zhukovskiy, V.I. and Salukvadze, M.E., Mnogokriterial’nye zadachi upravleniya v usloviyakh neopredelennosti (Multicriteria Control Problems under Uncertainty), Tbilisi: Metsniereba, 1991. 128 p. (in Russian). 6. Zhukovskiy, V.I. and Salukvadze, M.E., The Vector-Valued Maximin,New York: Academic Press, 1994, 404 p. 7. Zhukovskiy, V.I. and Salukvadze, M.E., Optimizatsiya garantii v mnogokrite- rial’nykh zadachakh upravleniya (Optimization of Guarantees in Multicriteria Control Problems), Tbilisi: Metsniereba, 1996. 475 p. (in Russian). 8. Zhukovskiy, V.I. and Salukvadze, M.E., Nekotorye igrovye
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