Game theory is a branch of mathematics devoted to the study of mathematical models used in decision making in situations involving conflict and cooperation. As a theory, it sheds a light on many aspects of the social and natural sciences and is based on an elegant and non-trivial mathematical theory. Game theory attempts to extract what is common and essential to situations of conflict, where different players have to make choices, by providing a normative guide to rational behavior for each of the players. Game theory thus goes beyond classical theories of probability and decision making involving just one player and chance. Modern game theory started in 1944 with a seminal work by von Neumann and Morgenstern. These authors presented many logical classifications of games and an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty. They also established the first optimal strategy in a two-person zero-sum games, which was generalized to n-person general-sum non-cooperative games in the Nobel awarded work by Nash. Game theory is now applied to many fields, such as economics, political science, management science, operations research, information theory, control theory, and evolutionary biology, as well as to pure mathematics. Non-cooperative games in normal form and Nash equilibria have been used in the study of many phenomena, including oligopolistic markets, bidding processes, electoral competition, resource allocation, and arms control. Major applications are to problems of cost allocation for public goods such as water resources, public transportation systems, and telephone systems.