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