Ciclo di seminari dipartimentali a. a. 2018/2019
When Stochastic Optimization meets Game Theory
Interviene: Abdel Lisser (Université Paris Sud)
Chance constrained optimization, also called probabilistic constrained optimization, is one of the main topics in stochastic optimization for dealing with random parameters in optimization problems. A chance constraint involving random parameters should hold with a prescribed probability which is in practice close to one. The use of chance constraints goes back to the late fifties. They have been widely applied in statistics, finance, engineering, energy planning etc. In this talk, we consider an n-player strategic game with a finite action set and random payoffs for each player. The payoff vector of each player follows a multivariate elliptically symmetric distribution. We assume that each player uses satisficing payoff criterion defined by a chance-constraint, i.e., players face a chance-constrained game. We show that there always exists a mixed strategy Nash equilibrium for this game. We also consider an n-player strategic game with random payoffs where the distribution of the payoff vector of each player is not completely known and belongs to a certain distributional uncertainty set. We formulate this game as a distributionally robust chance constrained game by defining a player's payoff function using a worst-case chance constraint. We show that there exists a mixed strategy Nash equilibrium for certain distributional uncertainty sets, and proposed an equivalent optimization problem for each case to compute the Nash equilibria.