11h30 - 11h55
Bifurcations in Two-Player Nonlinear Games Using Nonsmooth Dynamics and Variational Inequalities
It is known that Nash equilibrium points of a nonlinear 2-player game can be obtained by the equivalent reformulation of such a game into a variational inequality problem. In this work, we consider the case of a parameter being introduced in one or both of the players' payoffs. In this case the equivalent variational inequality problem becomes dependent on the payoffs' parameters. Furthermore the dynamics naturally associated to such a VI problem becomes a nonsmooth dynamical system whose right hand side will depend on the payoffs' parameter. Thus we are able to ask the question of whether bifurcations of the associated projected system take place, and what is the meaning of these bifurcations for the initial 2-player game. Once more Nash equilibria are established, the persistence and selection questions become pertinent for this set. We present our answers in this talk.
11h55 - 12h20
A variational inequality model for evaluating the security of supply in a natural gas supply chain
A large part of the European natural gas imports originates from unstable regions exposed to the risk of supply failure due to economical and political reasons. This has increased the concerns on the security of external supply in the European natural gas market. In this paper, we analyze the security of the external supply of the Italian gas market that mainly relies on imports to satisfy its gas demand. In particular, we develop a variational inequality model that describes the equilibrium state of a natural gas supply chain where producers, mid-streamers and consumers are exposed to this supply risk.
12h20 - 12h45
Generalized Nash equilibria and semi-infinite programming
Bilevel optimization, noncooperative games and semi-infinite programming share some similarities, which may lead to meaningful connections. Indeed, theoretical developments and algorithms developed for one of these models could be exploited to cope with the others. In this talk we focus on the relationships between generalized Nash games and semi-infinite programming. In particular, we show how generalized Nash games can be exploited to solve semi-infinite programs, relying on penalization techniques, nonsmooth optimization and a sequence of suitable saddlepoint problems.