Abstract

This course will provide the students with a solid understanding of theoretical, mathematical aspects and algorithms related to game theory, graph theory and social dynamics on networks for modelling the evolutionary dynamics of behaviours in real-world complex networks. The first lecture aims at introducing game theory and its basic notions, from the elements of a game, the normal form representation, the payoff matrix, and the concept of Nash Equilibrium. The second lecture deals with social dilemmas, evolutionary game theory and the rules for the evolution of cooperation. The third lecture describes the fundamental concepts, principles and methods of graph theory, network topologies, social networks and complex networks in the interdisciplinary field of network science. The fourth lecture focuses on dynamic processes on networks, including social dynamics and epidemic spreading on multilayer networks.