This project aims at developing mathematical models to describe the dynamics of large populations of interacting strategic agents. Detailed data concerning such phenomena are becoming increasingly available thanks to the unprecedented success of online social networks. Game-theoretic models provide a flexible mathematical framework and Nash equilibria should describe the long term behavior of such models. This research addresses several fundamental problems with this approach: Which of multiple Nash equilibria is selected? How rapidly does a system converge to such an equilibrium? How can one influence these dynamics? Leveraging recent advances in theoretical computer science, efficient algorithms will be developed to answer such questions.
The expression "social network" refers to a population of individuals together with their one-to-one social relationships (which can be of personal or economic nature). It is clear that the structure of such a network deeply affects the behavior of society as a whole (in particular, from the economic point of view). This intuition has never become practical or quantitative due to the lack of detailed data on the structure and dynamics of social networks. The Internet, and in particular the success of online social networking is dramatically changing this situation. This project aims at developing mathematical models and algorithms urgently needed to harness this data explosion. It will open the way to the application of economic analysis tools to this new arena, and thus facilitate new ways of exploiting online networks.
