Strategic Interactions and Mathematical Games: Models and Applications

Strategic interactions require planning and decision-making in contexts in which two or more players (agents) have to make choices in order to optimize one or more objectives. The players can have either a non-cooperative or a cooperative behaviour. The course reviews the main concepts of two-person zero- and non-zero-sum games, the role of cooperation, and cooperative N-person games. Then it focuses on cooperative games with transferable utility (TU games): their representation, the basic issues of stability and fairness, the related solution concepts, and the associated computational issues. N-person TU games provide extremely useful models, tools, and solution methodologies to disciplines including Economics, Engineering, Computer Science, Robotics, Political and Social Sciences, Biology, and Medicine. These links provide incentives for interdisciplinary research and make the role of mathematical games invaluable in a variety of applications. The course mainly focuses on applications and case studies from Engineering, which allow the students to see mathematical games “in action” in a variety of contexts. The role of approximation and machine learning to face computational issues in TU games is presented, too.