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.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
Game theory is a branch of modern applied mathematics that aims to analyze 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 this volume 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 n-person games are considered.
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.
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 book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.
This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.
This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.
This volume brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and the methodological aspects of game theory.
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