A multivalued approach offers effecient tools for dealing with game-theoretic models and analysing optima and economic equilibria. The goal of this project is to use the methods based on multivalued analysis and logics for the investigation of several selected challenging problems that arise in game theory. This will include both cooperative and non-cooperative games. We will analyse the stability and sensitivity of generalized Nash equilibrium problems and optimise the construction of the bidding strategy at the electricity spot market of the European Energy Exchange. A particular attention will be paid to solutions of cooperative games with fuzzy coalitions. New dynamic bargaining procedures for the core of such cooperative games will be developed. The applications of many-valued and dynamic epistemic logics will enable us to capture the flow of information and knowledge in games and to model the imprecision of data. The multivaluedness is present in all considered game models both on the side of the game description and the game solutions.