### Affiliations

University Paris Sud, France

## Plenary Session: On Chance Constrained Games

### Abstract

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 stochastic optimization, decisions are generally taken prior to the observation of the random events. This might lead to the violation of certain constraints which can be balanced by compensation actions also called recourse actions at later stages. When the recourse costs are known, a penalization function is introduced in the objective function. These models are called two-stage or multistage stochastic optimization problems. When the recourse actions are not available or cannot be considered due to some hard constraints for a given problem, decision-makers might be interested by solutions which could be infeasible for certain random parameters. In this case, chance constrained programs can be used efficiently.

In this talk, we consider an n-player strategic game with finite action set and random payoffs for each player. The payoff vector of each player either follows a multivariate elliptically symmetric distribution or defined within an uncertainty set. We assume that each player uses satisficing payoff criterion defined by a chance-constraint. We show that there exists a mixed strategy Nash equilibrium for this game. A mathematical formulation to compute the Nash equilibrium will be presented.

### Biography

Prof. Abdel Lisser received his PhD from University Paris Dauphine on interior point methods in 1987, and the habilitation thesis from University Paris Nord in 2000. His main research topics are stochastic optimization especially chance constrained optimization, conic optimization and stochastic game theory with applications mainly to telecommunication networks and energy management. He has been research engineer in Orange Labs for more than a decade. He is Full Professor at University Paris Sud since 2001, and Distinguished Professor since 2016 in the same University. He published several papers in leading journals and conferences, and is a member of some international journals and conferences boards.