Mathematical Equilibria: Applications, Models and Algorithms. An introduction.
Dr Giancarlo Bigi (Università di Pisa)
Wednesday 11th May, 2016 14:00-15:00 Maths 522
In scientific contexts the term "equilibrium" has been widely used at least in physics, chemistry, engineering and economics within different frameworks, relying on different mathematical models. For instance, it may refer to physical or mechanical structures, chemical processes, the distribution of traffic over computer and telecommunication networks or over public roads, portfolio selection, production competition, the economical dynamics of offer and demand. In this talk I will recall just a sample of them and show how they can be formulated through suitable mathematical models. In turn, many of these models (variational inequalities and noncooperative games among others) share an underlying common structure which allows to conveniently formulate them in a unique format, the so-called abstract equilibrium problem. This format is strongly related to mathematical optimization: I will briefly show the connections and how optimization algorithms can be exploited to compute equilibria.