Game Theory

The Special Issue “Game Theory” of the journal Mathematics provides a collection of papers that represent modern trends in mathematical game theory and its applications. The works address the problem of constructing and implementation of solution concepts based on classical optimality principles in different classes of games. In the case of non-cooperative behavior of players, the Nash equilibrium as a basic optimality principle is considered in both static and dynamic game settings. In the case of cooperative behavior of players, the situation is more complicated. As is seen from presented papers, the direct use of cooperative optimality principles in dynamic and differential games may bring time or subgame inconsistency of a solution which makes the cooperative schemes unsustainable. The notion of time or subgame consistency is crucial to the success of cooperation in a dynamic framework. In the works devoted to dynamic or differential games, this problem is analyzed and the special regularization procedures proposed to achieve time or subgame consistency of cooperative solutions. Among others, special attention in the presented book is paid to the construction of characteristic functions which determine the power of coalitions in games. The book contains many multi-disciplinary works applied to economic and environmental applications in a coherent manner

Subgame Consistent Cooperation [electronic resource] : A Comprehensive Treatise /

Strategic behavior in the human and social world has been increasingly recognized in theory and practice. It is well known that non-cooperative behavior could lead to suboptimal or even highly undesirable outcomes. Cooperation suggests the possibility of obtaining socially optimal solutions and the calls for cooperation are prevalent in real-life problems. Dynamic cooperation cannot be sustainable if there is no guarantee that the agreed upon optimality principle at the beginning is maintained throughout the cooperation duration. It is due to the lack of this kind of guarantees that cooperative schemes fail to last till its end or even fail to get started. The property of subgame consistency in cooperative dynamic games and the corresponding solution mechanism resolve this “classic” problem in game theory. This book is a comprehensive treatise on subgame consistent dynamic cooperation covering the up-to-date state of the art analyses in this important topic. It sets out to provide the theory, solution techniques and applications of subgame consistent cooperation in a wide spectrum of paradigms for analysis which includes cooperative dynamic game models with stochastic state dynamics, with uncertain future payoffs, with asynchronous players’ horizons, with random cooperation duration, with control spaces switching and with transferable and nontransferable payoffs. The book would be a significant research reference text for researchers in game theory, economists, applied mathematicians, policy-makers, corporate decision-makers, and graduate students in applied mathematics, game theory, decision sciences, economics and management sciences. "Technically this is a high quality book. It is very relevant to researchers of dynamic games – an area which is very relevant in nowadays research related to complex dynamic systems. The book provides original concepts, ideas and results with relevance." — Dusan Stipanovic “The 2004 Nobel Economics Prize was given to works in economic policies under the concept of time consistency with mathematical construction less general, rigorous and precise than that later developed in this book. The concept and technique of subgame consistency were just published then. In terms of advancement in practical applications this book is highly important theoretically and technically on top of economic interpretation.” — Vladimir Mazalov.Introduction -- Subgame Consistent Cooperative Solution in Differential Games -- Subgame Consistent Cooperation in Stochastic Differential Games -- Subgame Consistency in Randomly-Furcating Cooperative Stochastic Differential Games -- Subgame Consistency under Asynchronous Players’ Horizons -- Subgame Consistent Cooperative Solution in NTU Differential Games -- Subgame Consistent Cooperative Solution in Dynamic Games -- Subgame Consistent Cooperative Solution in Random Horizon Dynamic Games -- Subgame Consistency in Randomly-Furcating Cooperative Stochastic Dynamic Games -- Subgame Consistency under Furcating Payoffs, Stochastic Dynamics and Random Horizon -- Subgame Consistency in NTU Cooperative Dynamic Games -- Applications in Cooperative Public Goods Provision -- Collaborative Environmental Management -- Cooperation with Technology Switching -- Applications in Business Collaboration.Strategic behavior in the human and social world has been increasingly recognized in theory and practice. It is well known that non-cooperative behavior could lead to suboptimal or even highly undesirable outcomes. Cooperation suggests the possibility of obtaining socially optimal solutions and the calls for cooperation are prevalent in real-life problems. Dynamic cooperation cannot be sustainable if there is no guarantee that the agreed upon optimality principle at the beginning is maintained throughout the cooperation duration. It is due to the lack of this kind of guarantees that cooperative schemes fail to last till its end or even fail to get started. The property of subgame consistency in cooperative dynamic games and the corresponding solution mechanism resolve this “classic” problem in game theory. This book is a comprehensive treatise on subgame consistent dynamic cooperation covering the up-to-date state of the art analyses in this important topic. It sets out to provide the theory, solution techniques and applications of subgame consistent cooperation in a wide spectrum of paradigms for analysis which includes cooperative dynamic game models with stochastic state dynamics, with uncertain future payoffs, with asynchronous players’ horizons, with random cooperation duration, with control spaces switching and with transferable and nontransferable payoffs. The book would be a significant research reference text for researchers in game theory, economists, applied mathematicians, policy-makers, corporate decision-makers, and graduate students in applied mathematics, game theory, decision sciences, economics and management sciences. "Technically this is a high quality book. It is very relevant to researchers of dynamic games – an area which is very relevant in nowadays research related to complex dynamic systems. The book provides original concepts, ideas and results with relevance." — Dusan Stipanovic “The 2004 Nobel Economics Prize was given to works in economic policies under the concept of time consistency with mathematical construction less general, rigorous and precise than that later developed in this book. The concept and technique of subgame consistency were just published then. In terms of advancement in practical applications this book is highly important theoretically and technically on top of economic interpretation.” — Vladimir Mazalov