The classical optimal control theory deals with the determination of an optimal control that optimizes the criterion subjects to the dynamic constraint expressing the evolution of the system state under the influence of control variables. If this is extended to the case of multiple controllers (also called players) with different and sometimes conflicting optimization criteria (payoff function) it is possible to begin to explore differential games. Zero-sum differential games, also called differential games of pursuit, constitute the most developed part of differential games and are rigorously investigated. In this book, the full theory of differential games of pursuit with complete and partial information is developed. Numerous concrete pursuit-evasion games are solved ("life-line" games, simple pursuit games, etc.), and new time-consistent optimality principles in the n-person differential game theory are introduced and investigated.

Game theory is a branch of modern applied mathematics that aims to analyse various problems of conflict between parties that have opposed similar or simply different interests.Games are grouped into several classes according to some important features. In Game Theory (2nd Edition), Petrosyan and Zenkevich consider zero-sum two-person games, strategic N-person games in normal form, cooperative games, games in extensive form with complete and incomplete information, differential pursuit games and differential cooperative, and non-cooperative N-person games. The 2nd edition updates heavily from the 1st edition published in 1996.

This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

This book includes papers presented at the ISDG12-GTM2019 International Meeting on Game Theory, as a joint meeting of the 12th International ISDG Workshop and the 13th "International Conference on Game Theory and Management", held in St. Petersburg in July 2019. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

This book includes papers presented at the ISDG12-GTM2019 International Meeting on Game Theory, as a joint meeting of the 12th International ISDG Workshop and the 13th "International Conference on Game Theory and Management", held in St. Petersburg in July 2019. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on "Game Theory and Management" 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

This volume collects contributions from the talks given at the Game Theory and Management Conference held in St. Petersburg, Russia, in June 2017. It covers a wide spectrum of topics, among which are: game theory and management applications in fields such as: strategic management, industrial organization, marketing, operations and supply chain management, public management, financial management, human resources, energy and resource management, and others; cooperative games; dynamic games; evolutionary games; stochastic games.

This volume collects contributions from the talks given at the Game Theory and Management Conference held in St. Petersburg, Russia, in June 2017. It covers a wide spectrum of topics, among which are: game theory and management applications in fields such as: strategic management, industrial organization, marketing, operations and supply chain management, public management, financial management, human resources, energy and resource management, and others; cooperative games; dynamic games; evolutionary games; stochastic games.

This contributed volume contains fourteen papers based on selected presentations from the European Conference on Game Theory SING11-GTM 2015, held at Saint Petersburg State University in July 2015, and the Networking Games and Management workshop, held at the Karelian Research Centre of the Russian Academy of Sciences in Petrozvavodsk, Russia, also in July 2015. These papers cover a wide range of topics in game theory, including recent advances in areas with high potential for future work, as well as new developments on classical results. Some of these include A new approach to journal ranking using methods from social choice theory; A differential game of a duopoly in which two firms are competing for market share in an industry with network externalities; The impact of information propagation in the model of tax audits; A voting model in which the results of previous votes can affect the process of coalition formation in a decision-making body; The Selten-Szidarovsky technique for the analysis of Nash equilibria of games with an aggregative structure; Generalized nucleoli and generalized bargaining sets for games with restricted cooperation; Bayesian networks and games of deterrence; and A new look at the study of solutions for games in partition function form. The maturity and vitality of modern-day game theory are reflected in the new ideas, novel applications, and contributions of young researchers represented in this collection. It will be of interest to anyone doing theoretical research in game theory or working on one its numerous applications.

This contributed volume contains fourteen papers based on selected presentations from the European Conference on Game Theory SING11-GTM 2015, held at Saint Petersburg State University in July 2015, and the Networking Games and Management workshop, held at the Karelian Research Centre of the Russian Academy of Sciences in Petrozvavodsk, Russia, also in July 2015. These papers cover a wide range of topics in game theory, including recent advances in areas with high potential for future work, as well as new developments on classical results. Some of these include A new approach to journal ranking using methods from social choice theory; A differential game of a duopoly in which two firms are competing for market share in an industry with network externalities; The impact of information propagation in the model of tax audits; A voting model in which the results of previous votes can affect the process of coalition formation in a decision-making body; The Selten-Szidarovsky technique for the analysis of Nash equilibria of games with an aggregative structure; Generalized nucleoli and generalized bargaining sets for games with restricted cooperation; Bayesian networks and games of deterrence; and A new look at the study of solutions for games in partition function form. The maturity and vitality of modern-day game theory are reflected in the new ideas, novel applications, and contributions of young researchers represented in this collection. It will be of interest to anyone doing theoretical research in game theory or working on one its numerous applications.

Various imperfections in existing market systems prevent the free market from serving as a truly efficient allocation mechanism, but optimization of economic activities provides an effective remedial measure. Cooperative optimization claims that socially optimal and individually rational solutions to decision problems involving strategic action over time exist. To ensure that cooperation will last throughout the agreement period, however, the stringent condition of subgame consistency is required.

This textbook presents a study of subgame consistent economic optimization, developing game-theoretic optimization techniques to establish the foundation for an effective policy menu to tackle the suboptimal behavior that the conventional market mechanism fails to resolve.

This is a collection of recent novel contributions in game theory from a group of prominent authors in the field. It covers Non-cooperative Games, Equilibrium Analysis, Cooperative Games and Axiomatic Values in static and dynamic contexts.Part 1: Non-cooperative Games and Equilibrium AnalysisIn game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing (e.g. through credible threats) alliances (or competition between groups of players, called 'coalitions') are possible due to the absence of external means to enforce cooperative behavior (e.g. contract law), as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players' individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. This volume on non-cooperative games and equilibrium analysis contains a variety of non-cooperative games and non-cooperative game equilibria from prominent authors in the field.Part 2: Cooperative Games and Axiomatic ValuesIt is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like the prisoner's dilemma) and even devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. This volume on cooperative games and axiomatic values presents a collection of cooperative games and axiomatic values from prominent authors in the field.

Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics. "Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dušan M Stipanović, Professor, University of Illinois at Urbana-Champaign  "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College “Durable-strategies Dynamic Games is truly a world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies.� Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games 

Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics. "Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dusan M Stipanovic, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College "Durable-strategies Dynamic Games is truly a world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies." Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games

This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on "Game Theory and Management" 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

After several decades of rapid technological advancement and economic growth, alarming levels of pollution and catastrophe-bound environmental degradations are emerging all over the world. Even sizable reduction in industrial pollutant emissions would only slow down the accumulation of pollution. Given the complexity of the problem and the over-simplicity of international environmental initiatives (like the Kyoto Protocol, Montreal Protocol and Paris Agreement, which focused mainly on emissions reduction and regulations), limited success has been observed. The design of a comprehensive solution for solving this globally devastating problem is very much in order. Research in developing environmentally clean technology into efficient and affordable means of production plays a key role to effectively solving the continual worsening global industrial pollution problem and meeting the industrial growth needs. An essential element for success is that the participating nations well-being must not be worse than their non-cooperative well-being throughout the cooperation duration. In addition, for the cooperative scheme to be sustainable, the agreed-upon optimality principle in sharing the cooperative benefits must be upheld at every stage of the cooperation plan -- this condition is known as subgame consistency. This book provides an effective means for resolving the catastrophe-bound environmental problem through a Building Environmentally Sustainable Technology with Subgame Consistent, Optimal, Rational and Economically-viable Scheme (BEST SCORES). In particular, the solution scheme involves: (i) A set of policy instruments which includes levies on industrial pollution, royalties on natural resources, coordinated pollutant abatement efforts, cooperative development of clean technology, and transfer payments leading to an optimal cooperation solution; (ii) Joint development of environmentally sustainable technology and an optimal technology pattern over time; (iii) A cooperative maximisation program yielding the optimal (highest) joint payoff; (iv) An economically viable scheme for each participating nation with a cooperative payoff higher than its non-cooperative payoff through transfer payments; (v) A subgame consistent payoff distribution procedure, which ensures that the original agreed upon optimality principle in gain sharing will be maintainedl; (vi) An institutional mechanism design to guide the construction of relevant institutions and agencies to implement the cooperative scheme.

Economics is a science which studies human behaviours as a relationship between ends and scarce means which have alternative uses. Since economic resources are scarce, optimisation forms an integral part in the study of economics. In addition, in the presence of imperfect market structure, externalities, imperfect information or public goods, the market fails to provide an efficient allocation mechanism. Optimisation of economic activities provides an effective remedial measure for market failures. This contributed volume collects advances in the studies of economics and optimisation. Contributions cover areas on analysis of optimal allocation of economic resources, economic optimisation techniques, the interface economics and optimisation, optimisation under market mechanism and history of development of optimisation techniques. The studies assembled in this volume are dedicated to the memory of a pioneering researcher and Nobel Laureate in the field of economic optimisation -- Leonid Vitalyevich Kantorovich. In his 100th birthday tribute in 2012, the International Conference Mathematics, Economic, Management: Kantorovich-100 in St-Petersburg was held in his memory. Selected papers from the conference are included in this Volume. In addition, contributed papers from authors who had worked closely with Kantorovich are also contained.