Thermodynamic limit and phase transitions in non-cooperative games: some mean-ﬁeld examples
16th November 2018, 3:30 pm – 4:30 pm
Main Maths Building, SM4
In stochastic dynamics inspired by Statistical Mechanics the interaction between diﬀerent particles, or agents, is usually expressed as a given function of their states. The behavior of the system, in the limit of inﬁnitely many particles (thermodynamic limit), may change dramatically by small changes in the parameters of the model: when this occurs we say there is a phase transition. In many applications the interaction cannot be given a priori but it is rather a result of agents’ strategy, aimed at optimizing a given performance. Using the simplest models of this nature, mean ﬁeld games, we illustrate some examples of phase transitions, pointing to diﬃculties in the proof of the thermodynamic limit.