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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.

Research & information: general --- Mathematics & science --- pursuit --- control functions --- integral constraints --- strategies --- value of the game --- decision-making --- game theory --- project management --- differential games --- cooperative differential games --- Time Consistency --- IDP-core --- IDP dominance --- two-sided platform market --- pricing --- Hotelling’s duopoly on the plane --- Nash equilibrium --- optimal location of platforms --- prescribed duration --- characteristic function --- environmental resource management --- pollution control --- discrete-time games --- cooperation --- the core --- linear transformation --- time consistency --- multistage game --- chance moves --- subgame perfect equilibria --- cooperative trajectory --- imputation distribution procedure --- random time horizon --- time until failure --- discounted equilibrium --- weibull distribution --- chen distribution --- equivalence principle --- cooperative game --- satisfaction criteria --- proportional value --- axiomatization --- cooperative stochastic game --- strong subgame consistency --- core --- dynamic games --- multicriteria games --- Nash bargaining solution --- dynamic stability --- rational behavior conditions --- Shapley-Solidarity value --- coalition structure --- potential --- bidding mechanism