Mathematical Game Theory

Dear Colleagues,

Rapid developments in technology, communication, industrial organization, economic integration and international trade have stimulated the appearance of different practical statements in the description of agent interaction, based on the game theory. A strategic approach to decision-making is very useful in many areas, such as bargaining, resource allocation, fishery, competition and cooperation, pollution control, networking, and competitive mobile systems. The main tools in the analysis of game models are mathematical methods. In dynamic games, the Hamilton-Jacobi-Bellman equation and Pontryagin maximum principle are very useful. Dynamic games theory has many applications in many fields, including biology, computer science, ecology, economics and management. In networking games, the result of interactions between agents are defined by a certain network. Networking games are games on graphs; graph-theoretic models are very important in this field.  This direction in game theory has appeared in connection with the emergence of new information technologies. First of all it's the global Internet, mobile communications, distributed and cloud computing and social networks. In routing games, players choose information transfer channels with limited bandwidths.  Equilibrium, here, is a result of the application of the optimization theory.  Social networks appear lead to many new game-theoretic problem formulations. Users of such networks are united in communities, forming networks of different topologies. An analysis of the structure of such a graph is important in of itself, but is also important in being able to evaluate the results of equilibrium game-theoretic interactions in such networks. The spectrum of mathematical approaches in game theory is very wide.

This Special Issue contains papers that cover the wide range of mathematical methods used in game theory, including recent advances in areas of high potential for future works, as well as new developments in classical results. It will be of interest to anyone doing theoretical research in game theory or working on one its numerous applications.

Prof. Dr. Vladimir Mazalov
Guest Editor

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