Annals of the International Society of Dynamic Games – serie

Recent years have witnessed a surge of activity in the field of dynamic games, in both theory and applicati( s. Th well as practical problems in zero-sum and nonzero-sum games, continuous time differential games and discrete time multistage games, and deterministic and stochastic games are currently being investigated by researchers in diverse disciplines, such as engineering, mathematics, biology, economics, management science, and political science. 'Mis surge of interest led, in 1990, to the formation of the International Society of Dynamic Gaines (ISDG), whose primary goal is to foster the development of advanced research and applications in the field of game theory. One important activity of the Society is to hold a biannual, intemational symposium to bring together researchers who contribute to the development of this active field of applied science. In 1992 such a symposium was held in Grimentz, Switzerland. This book, which is the first volume in the new series, Annals of Dynamic Gaines, is based on selected presentations made at this symposium. It is, however, not simply a book of proceedings for a conference.EveTy paper that appears in this volume has passed through a selective refereeing proem, as in an archival technical joumal. This makes this first volume of the Annals of Dynamic Games a quality publication that presents a timely account of the state-of-the-all in this dynamic field. The papers included in this volume attest to the vitality and diversity of ongoing research in dynamic games and applications. The reader wfll fmd here important contributions in the following five areas, which also constitute the groups according to which the twenty-three chapters have been organized: Robust control design and H'-theory; pursuit-evasion games and numerical schemes; numerical solutions of discrete time games, based on mathematical programming techniques; stochastic differential, sequential and Markov games; and applications in ecology, environmental management, and biology. With such diversity of topics, the book should be a valuable resource for researchers in the field of dynamic games and all neighboring disciplines.

The theory of dynamic games is very rich in nature and very much alive! If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec­ tively difference equations) and games based on Markov chains, with determin­ istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica­ tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes.

This work focuses on the application of dynamic game theory and control theory to analyze a number of important issues in the interaction between economic and environmental problems. The authors provide research results, mathematical models and prescriptions for public policy tools to prevent economic and natural systems from taking unsustainable development paths. The book should be of interest to research workers in industry and university, including engineers, mathematicians, economists and public policy-makers.

Modem game theory has evolved enonnously since its inception in the 1920s in the works ofBorel and von Neumann and since publication in the 1940s of the seminal treatise "Theory of Games and Economic Behavior" by von Neumann and Morgenstern. The branch of game theory known as dynamic games is-to a significant extent-descended from the pioneering work on differential games done by Isaacs in the 1950s and 1960s. Since those early decades game theory has branched out in many directions, spanning such diverse disciplines as math- ematics, economics, electrical and electronics engineering, operations research, computer science, theoretical ecology, environmental science, and even political science. The papers in this volume reflect both the maturity and the vitalityofmodem day game theoryin general, andofdynamic games, inparticular. The maturitycan be seen from the sophistication ofthe theorems, proofs, methods, and numerical algorithms contained in these articles.The vitality is manifested by the range of new ideas, new applications, the numberofyoung researchers among the authors, and the expanding worldwide coverage of research centers and institutes where the contributions originated.

The theory of two-person, zero-sum differential games started at the be- ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton- Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe- sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv- ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I.Subbotin (see their book Po- sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.

Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man­ aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so­ cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con­ trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica­ tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a guide to the vitality and growth of the field. A valuable reference for researchers and practitioners in dynamic game theory, it covers a broad range of topics and applications, including repeated and stochastic games, differential dynamic games, optimal stopping games, and numerical methods and algorithms for solving dynamic games. The diverse topics included will also benefit researchers and graduate students in applied mathematics, economics, engineering, systems and control, and environmental science.

The theory of dynamic games continues to evolve, and one purpose of this volume is to report a number of recent theoretical advances in the ?eld, which are covered in Parts I, II and IV. Another aim of this work is to present some new applications of dynamic games in various areas, including pursuit-evasion games (Part III), ecology (Part IV), and economics (Part V). The volume concludes with a number of contributions in the ?eld of numerical methods and algorithms in dynamic games (Part VI). With a single exception, the contributions of this volume are outgrowths of talks that were presented at the Eleventh International Symposium on Dynamic Games and Applications, held in Tucson, Arizona, USA, in December 2004, and organized by the International Society of Dynamic Games. The symposium was co-sponsored by the University of Arizona, College of Engineering and Aerospace and Mechanical Engineering, as well as GERAD, Montréal, Canada, and the ISDG Organizing Society. The volume contains thirty-?ve chapters that have been peer-reviewed according to the standards of international journals in game theory and applications. Part I deals with the theory of dynamic games and contains six chapters. Cardaliaguet, Quincampoix, and Saint-Pierre provide a survey of the state-- the-art of the use of viability theory in the formulation and analysis of differential games, in particular zero-sum games. An important result of viability theory is that many zero-sum differential games can be formulated as viability problems.

The paradigms of dynamic games play an important role in the development of multi-agent models in engineering, economics, and management science. The applicability of their concepts stems from the ability to encompass situations with uncertainty, incomplete information, fluctuating coalition structure, and coupled constraints imposed on the strategies of all the players. This book—an outgrowth of the 10th International Symposium on Dynamic Games—presents current developments of the theory of dynamic games and its applications to various domains, in particular energy-environment economics and management sciences. This work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.

This book presents current advances in the theory of dynamic games and their applications in several disciplines. The selected contributions cover a variety of topics ranging from purely theoretical developments in game theory, to numerical analysis of various dynamic games, and then progressing to applications of dynamic games in economics, finance, and energy supply. Thematically organized into eight parts, the book covers key topics in these main areas: theoretical developments in general dynamic and differential games, pursuit-evasion games, numerical approaches to dynamic and differential games, applications of dynamic games in economics and option pricing, search games, evolutionary games, stopping games, and stochastic games and "large neighborhood" games.A unified collection of state-of-the-art advances in theoretical and numerical analysis of dynamic games and their applications, the work is suitable for researchers, practitioners, and graduate students in applied mathematics, engineering, economics, as well as environmental and management sciences.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.Featured throughout are useful tools and valuable resources for researchers, practitioners, and graduate students interested in dynamic games and their applications in applied mathematics, engineering, economics, and management science. Also included in the volume is a special tribute to Arik Melikyan, honoring his memory and the many contributions he made to the field of dynamic games.

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 14th International Symposium of Dynamic Games and Applications held in Banff. Advances in Dynamic Games covers a variety of topics, ranging from evolutionary games, theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as mathematical biology, environmental management, finance and economics, engineering, guidance and control, and social interaction. Featured throughout are valuable tools and resources for researchers, practitioners, and graduate students interested in dynamic games and their applications to mathematics, engineering, economics, and management science.​

Game theory is a rich and active area of research of which this new volume of the Annals of the International Society of Dynamic Games is yet fresh evidence. Since the second half of the 20th century, the area of dynamic games has man­ aged to attract outstanding mathematicians, who found exciting open questions requiring tools from a wide variety of mathematical disciplines; economists, so­ cial and political scientists, who used game theory to model and study competition and cooperative behavior; and engineers, who used games in computer sciences, telecommunications, and other areas. The contents of this volume are primarily based on selected presentation made at the 8th International Symposium of Dynamic Games and Applications, held in Chateau Vaalsbroek, Maastricht, the Netherlands, July 5-8, 1998; this conference took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. The conference has been cosponsored by the Control Systems Society of the IEEE, IFAC (International Federation of Automatic Con­ trol), INRIA (Institute National de Recherche en Informatique et Automatique), and the University of Maastricht. One ofthe activities of the ISDG is the publica­ tion of the Annals. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival journals.

Recent years have witnessed a surge of activity in the field of dynamic both theory and applications. Theoretical as well as practical games, in problems in zero-sum and nonzero-sum games, continuous time differential and discrete time multistage games, and deterministic and stochastic games games are currently being investigated by researchers in diverse disciplines, such as engineering, mathematics, biology, economics, management science, and political science. This surge of interest has led to the formation of the International Society of Dynamic Games (ISDG) in 1990, whose primary goal is to foster the development of advanced research and applications in the field of game theory. One important activity of the Society is to organize biannually an international symposium which aims at bringing together all those who contribute to the development of this active field of applied science. In 1992 the symposium was organized in Grimentz, Switzerland, under the supervision of an international scientific committee and with the help of a local organizing committee based at University of Geneva. This book, which is the first volume in the new Series, Annals of the International Society of Dynamic Games (see the Preface to the Series), is based on presentations made at this symposium. It is however more than a book of proceedings for a conference. Every paper published in this volume has passed through a very selective refereeing process, as in an archival technical journal.

This book collects some recent works on the application of dynamic game and control theory to the analysis of environmental problems. This collec­ tion of papers is not the outcome of a conference or of a workshop. It is rather the result of a careful screening from among a number of contribu­ tions that we have solicited across the world. In particular, we have been able to attract the work of some of the most prominent scholars in the field of dynamic analyses of the environment. Engineers, mathematicians and economists provide their views and analytical tools to better interpret the interactions between economic and environmental phenomena, thus achiev­ ing, through this interdisciplinary effort, new and interesting results. The goal of the book is more normative than descriptive. All papers include careful modelling of the dynamics of the main variables involved in the game between nature and economic agents and among economic agents themselves, as well-described in Vrieze's introductory chapter. Fur­ thermore, all papers use this careful modelling framework to provide policy prescriptions to the public agencies authorized to regulate emission dy­ namics. Several diverse problems are addressed: from global issues, such as the greenhouse effect or deforestation, to international ones, such as the management of fisheries, to local ones, for example, the control of effluent discharges. Moreover, pollution problems are not the only concern of this book.

Modem game theory has evolved enonnously since its inception in the 1920s in the works ofBorel and von Neumann and since publication in the 1940s of the seminal treatise "Theory of Games and Economic Behavior" by von Neumann and Morgenstern. The branch of game theory known as dynamic games is-to a significant extent-descended from the pioneering work on differential games done by Isaacs in the 1950s and 1960s. Since those early decades game theory has branched out in many directions, spanning such diverse disciplines as math- ematics, economics, electrical and electronics engineering, operations research, computer science, theoretical ecology, environmental science, and even political science. The papers in this volume reflect both the maturity and the vitalityofmodem day game theoryin general, andofdynamic games, inparticular. The maturitycan be seen from the sophistication ofthe theorems, proofs, methods, and numerical algorithms contained in these articles.The vitality is manifested by the range of new ideas, new applications, the numberofyoung researchers among the authors, and the expanding worldwide coverage of research centers and institutes where the contributions originated.

The theory of two-person, zero-sum differential games started at the be- ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton- Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe- sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv- ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I.Subbotin (see their book Po- sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.

The theory of dynamic games is very rich in nature and very much alive! If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec­ tively difference equations) and games based on Markov chains, with determin­ istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica­ tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes.

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environmentsModels for climate change negotiationsNash Equilibria for dynamic games involving Volterra integral equationsDifferential games in healthcare marketsLinear-quadratic Gaussian dynamic gamesAircraft control in wind shear conditionsAdvances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.

This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers with paths to further research, serving as a testimony to the vitality of the field. Experts cover a range of theory and applications related to games and dynamic games, with topics including:Dynamically stable cooperative provision of public goods under non-transferable utilityStrongly time-consistent solutions in cooperative dynamic gamesIncentive Stackelberg games for stochastic systemsStatic and inverse Stackelberg games in political economyCournot and Betrand competition on symmetric R&D networksNumerical Nash equilibria using curvilinear multistart algorithmMarkov chain approximation numerical scheme for infinite-horizon mean field gamesFrontiers in Games and Dynamic Games will appeal to an interdisciplinary audience of researchers, practitioners, and graduate students interested in games and dynamic games.

This contributed volume presents the state-of-the-art of games and dynamic games, featuring several chapters based on plenary sessions at the ISDG-China Chapter Conference on Dynamic Games and Game Theoretic Analysis, which was held from August 3-5, 2017 at the Ningbo campus of the University of Nottingham, China. The chapters in this volume will provide readers with paths to further research, serving as a testimony to the vitality of the field. Experts cover a range of theory and applications related to games and dynamic games, with topics including:Dynamically stable cooperative provision of public goods under non-transferable utilityStrongly time-consistent solutions in cooperative dynamic gamesIncentive Stackelberg games for stochastic systemsStatic and inverse Stackelberg games in political economyCournot and Betrand competition on symmetric R&D networksNumerical Nash equilibria using curvilinear multistart algorithmMarkov chain approximation numerical scheme for infinite-horizon mean field gamesFrontiers in Games and Dynamic Games will appeal to an interdisciplinary audience of researchers, practitioners, and graduate students interested in games and dynamic games.

This contributed volume collects talks originally given at the 18th International Symposium on Dynamic Games and Applications, held in Grenoble, France from July 9-12, 2018. Chapters present state-of-the-art research in the field of dynamic games and are written by leading experts in this active area. Featuring a broad overview of recent advances as well as a wide range of applications, this book is organized into four sections: games of conflict, evolutionary games, economic games, and games involving common interest. Within these sections, specific topics covered include:Pursuit-evasion gamesPartnership formation gamesReplicator dynamicsLoad balancing congestion gamesEquilibrium coalition structuresAdvances in Dynamic Games will be of particular interest to researchers and doctoral students studying game theory.

This contributed volume collects talks originally given at the 18th International Symposium on Dynamic Games and Applications, held in Grenoble, France from July 9-12, 2018. Chapters present state-of-the-art research in the field of dynamic games and are written by leading experts in this active area. Featuring a broad overview of recent advances as well as a wide range of applications, this book is organized into four sections: games of conflict, evolutionary games, economic games, and games involving common interest. Within these sections, specific topics covered include:Pursuit-evasion gamesPartnership formation gamesReplicator dynamicsLoad balancing congestion gamesEquilibrium coalition structuresAdvances in Dynamic Games will be of particular interest to researchers and doctoral students studying game theory.

This contributed volume collects overviews and recent advances in dynamic games and their applications, based on presentations given at the 19th and 20th International Symposium in Dynamic Games and Applications, held July 25-28, 2022, in Porto, Portugal, and July 9-12, 2024, in Valladolid, Spain. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including differential games, mean field games, repeated games, evolutionary games, and search games; applications of dynamic game theory to economic growth, supply chain management, advertising, and climate change, as well as an experimental investigation of how games are played.Advances in Dynamic Games presents state-of-the-art research in a wide spectrum of areas. As such, it testifies to the continued vitality and growth of the field of dynamic games and applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.

This contributed volume focuses on aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. It covers theoretical developments, algorithmic methods, and applications to fields as varied as mathematical biology, environmental management, economics, engineering, guidance and control, and social interaction. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.Advances in Dynamic Games presents state-of-the-art research that serves as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 15th International Symposium of Dynamic Games and Applications held July 19–22, 2012, in Byšice, Czech Republic.

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 16th Symposium of the International Society of Dynamic Games, held July 9-12, 2014, in Amsterdam. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. They discuss theoretical developments, algorithmic methods, issues relating to lack of information, and applications in areas such as biological or economical competition, stability in communication networks, and maintenance decisions in an electricity market, just to name a few.Advances in Dynamic and Evolutionary Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.

This contributed volume focuses on aspects of dynamic game theory including differential games, evolutionary games, and stochastic games. It covers theoretical developments, algorithmic methods, and applications to fields as varied as mathematical biology, environmental management, economics, engineering, guidance and control, and social interaction. It will be of interest to an interdisciplinary audience of researchers, practitioners, and advanced graduate students.Advances in Dynamic Games presents state-of-the-art research that serves as a testament to the vitality and growth of the field of dynamic games and their applications. Its contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 15th International Symposium of Dynamic Games and Applications held July 19–22, 2012, in Byšice, Czech Republic.

This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environmentsModels for climate change negotiationsNash Equilibria for dynamic games involving Volterra integral equationsDifferential games in healthcare marketsLinear-quadratic Gaussian dynamic gamesAircraft control in wind shear conditionsAdvances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.