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Static & Dynamic Game Theory: Foundations & Applications Leon A. Petrosyan Vladimir V. Mazalov Nikolay A. Zenkevich Editors Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2017 Static & Dynamic Game Theory: Foundations & Applications Series Editor Tamer Bas¸ar, 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 Leon A. Petrosyan • Vladimir V. Mazalov • Nikolay A. Zenkevich Editors Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2017 Editors Leon A. Petrosyan Vladimir V. Mazalov St. Petersburg State University Institute of Applied Mathematical Research St. Petersburg, Russia Karelian Research Center of RAS Petrozavodsk, Russia Nikolay A. Zenkevich Graduate School of Management St. Petersburg State University St. Petersburg, Russia ISSN 2363-8516 ISSN 2363-8524 (electronic) Static & Dynamic Game Theory: Foundations & Applications ISBN 978-3-319-92987-3 ISBN 978-3-319-92988-0 (eBook) https://doi.org/10.1007/978-3-319-92988-0 Library of Congress Control Number: 2018950064 © Springer International Publishing AG, part of Springer Nature 2018 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, express 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. Printed on acid-free paper This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface Game theory is an area of applied mathematics that models the interaction between agents (called players) to find the optimal behavior that each player has to adopt to maximize his or her reward when such prize depends not only on the individual choices of a player (or a group of players) but also on the decisions of all agents involved in the system. Nowadays, game theory is an extremely important tool for economic theory and has contributed to a better understanding of human behavior in the process of decision-making in situations of conflict. In its beginnings, game theory was a tool to understand the behavior of economic systems, but currently it is used in many fields, such as biology, sociology, political science, military strategy, psychology, philosophy and computer science. In all these areas, game theory is perhaps the most sophisticated and fertile paradigm that applied mathematics can offer to analyze the process of making a decision under real-world conditions. The conflicts between rational beings that distrust each other, or between com- petitors that interact and influence each other, constitute the object of study of game theory. Such studies are based on rigorous mathematical analyses; nevertheless, they arise naturally from the observation of a conflict from a rational point of view. For the theorists in our field, a “game” is a conflictive situation in which competing interests of individuals or institutions prevail, and in that context, each party influences the decisions that the others will make; thus, the result of the conflict is determined by the decisions taken by all the actors. In the so-called canonical form, a game takes place when an individual pursues an objective when other individuals concurrently pursue other (overlapping or conflicting) objectives, and in the same time these objectives cannot be reached by individual actions of one decision maker. The problem is to determine each player’s optimal decision (with respect to some predetermined criterion), how such decisions interact among each other, and what are the properties of the outcome brought about by these choices. The contents of this volume are primarily based on selected talks presented at the 11th International Conference “Game Theory and Management” 2017 (GTM2017) held in Saint Petersburg State University, in Saint Petersburg, Russia, from 28 to 30 June 2017. Each chapter in this volume has passed a rigorous reviewing process, v vi Preface as is the case for the journals on applied mathematics. It is worth mentioning that the predecessors of this conference (GTM2007-GTM2016) were held in Saint Petersburg State University and were supported by the International Society of Dynamic Games—Russian Chapter. The conference unites the game theorists of two schools: the classical school founded by J. V. Neumann and O. Morgenstern, and the school of differential games first introduced by R. Isaacs. GTM has succeeded to achieve this goal along the years, and this can be seen by taking a look at the list of our plenary speakers: R. Aumann, T. Bashar, G. J. Olsder, J. Nash, R. Selten, F. Kidland, R. Myerson, D. W. K. Yeung, G. Zaccour, E. Maskin, S. Jorgensen, D. Schmeidler, A. Tarasyev, H. Moulin, D. Novikov, A. Haurie, G. Owen, A. Newman, P. Bernhard, J. Weibull, B. Monien, S. Zamir, S. Aseev, S. Hart, M. Breton, R. Laraki, and others (among whom the authors of this preface have the honor to appear). The present volume proves that GTM offers an interactive program on a wide range of the latest developments in game theory and management. It includes recent advances in topics with high future potential and existing developments in classical fields. I wish to thank all of the associate editors and reviewers for their outstanding contribution. Without them, this book would have not been possible. St. Petersburg, Russia Leon A. Petrosyan Petrozavodsk, Russia Vladimir V. Mazalov St. Petersburg, Russia Nikolay A. Zenkevich March, 2018 Contents 1 Countervailing Power with Large and Small Retailers . . . . . . . . . . . . . . . . 1 George Geronikolaou and Konstantinos G. Papadopoulos 2 Dynamic Voluntary Provision of Public Goods: The Recursive Nash Bargaining Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Simon Hoof 3 Altruistic, Aggressive and Paradoxical Types of Behavior in a Differential Two-Person Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Anatolii Kleimenov 4 Learning in a Game of Strategic Experimentation with Three-Armed Exponential Bandits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Nicolas Klein 5 Solution for a System of Hamilton–Jacobi Equations of Special Type and a Link with Nash Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Ekaterina A. Kolpakova 6 The Impact of Discounted Indices on Equilibrium Strategies of Players in Dynamical Bimatrix Games. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Nikolay Krasovskii and Alexander Tarasyev 7 On Control Reconstruction Problems for Dynamic Systems Linear in Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Evgeniy Krupennikov 8 Evolution of Risk-Statuses in One Model of Tax Control . . . . . . . . . . . . . . 121 Suriya Kumacheva, Elena Gubar, Ekaterina Zhitkova, and Galina Tomilina 9 Stationary Nash Equilibria for Average Stochastic Positional Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Dmitrii Lozovanu vii viii Contents 10 Game Equilibria and Transition Dynamics in Networks with Heterogeneous Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Vladimir Matveenko, Maria Garmash, and Alexei Korolev 11 Non-cooperative Differential Game Model of Oil Market with Looking Forward Approach .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Ovanes Petrosian, Maria Nastych, and Dmitrii Volf 12 S-strongly Time-Consistency in Differential Games. . . . . . . . . . . . . . . . . . . . 203 Leon A. Petrosyan and Ekaterina V. Gromova 13 Characteristic Functions in a Linear Oligopoly TU Game . . . . . . . . . . . . 219 Artem Sedakov 14 The Position Value and the Myerson Value for Hypergraph Communication Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Erfang Shan and Guang Zhang 15 Bertrand Meets Ford: Benefits and Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Alexander Sidorov, Mathieu Parenti, and Jacques-Francois Thisse 16 On Multilateral Hierarchical Dynamic Decisions. . . . . . . . . . . . . . . . . . . . . . . 269 Krzysztof Szajowski Contributors Maria Garmash National Research University Higher School of Economics, St. Petersburg, Russia George Geronikolaou Democritus University of Thrace, Komotini, Greece Ekaterina V. Gromova Saint Petersburg State University, Saint Petersburg, Russia Elena Gubar Saint Petersburg State University, Saint Petersburg, Russia Simon Hoof Paderborn University, Department of Economics, Paderborn, Ger- many Anatolii Kleimenov Krasovskii Institute of Mathematics and Mechanics UrB RAS, Yekaterinburg, Russia Nicolas Klein Université de Montréal and CIREQ, Département de Sciences Économiques, Montréal, QC, Canada Ekaterina A. Kolpakova Krasovskii Institute of Mathematics and Mechanics UrB RAS, Yekaterinburg, Russia Alexei Korolev National Research University Higher School of Economics, St. Petersburg, Russia Nikolay Krasovskii Krasovskii Institute of Mathematics and Mechanics UrB RAS, Yekaterinburg, Russia Evgeniy Krupennikov Krasovskii Institute of Mathematics and Mechanics UrB RAS, Yekaterinburg, Russia Ural Federal University, Yekaterinburg, Russia Suriya Kumacheva Saint Petersburg State University, Saint Petersburg, Russia Dmitrii Lozovanu Institute of Mathematics and Computer Science of Moldova Academy of Sciences, Chisinau, Moldova ix
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