Game Theory

This text provides a discussion of some relevant topics in game theory. It is composed partially from material compiled by Professor Joachim Rosenmuller when lecturing at IMW, the Institute of Mathematical Economics at the University of Bielefeld. It also contains research topics that are not presented in a typical game theory textbook. The volume has a non-co-operative and a co-operative part and in both of them the reader is assumed to have some basic knowledge in game theory, for instance, concerning the normal form (bimatrix games, Nash equilibria of the mixed extension, backwards induction in games with perfect information) and the coalitional function (simple games, convex games, superadditive games, the core, the Shapley volume). Some emphasis is laid on the probabilistic background; however, the author treats stochastic games using the language of probability in order to consider simple models in which measure theory can be omitted.