Friday, 10:30 - 10:55 h, Room: MA 005

 

Ming Hu
Existence, uniqueness, and computation of robust Nash equilibrium in a class of multi-leader-follower games

Coauthor: Masao Fukushima

 

Abstract:
The multi-leader-follower game can be looked on as a generalization of the Nash equilibrium problem (NEP), which contains several leaders and followers. On the other hand, in such real-world problems, uncertainty normally exists and sometimes cannot simply be ignored. To handle mathematical programming problems with uncertainty, the robust optimization (RO) technique assumes that the uncertain data belong to some sets, and the objective function is minimized with respect to the worst case scenario. In this paper, we focus on a class of multi-leader-follower games under uncertainty with some special structure. We particularly assume that the follower's problem only contains equality constraints. By means of the RO technique, we first formulate the game as the robust Nash equilibrium problem, and then the generalized variational inequality (GVI) problem. We then establish some results on the existence and uniqueness of a robust leader-follower Nash equilibrium. We also apply the forward-backward splitting method to solve the GVI formulation of the problem and present some numerical examples to illustrate the behavior of robust Nash equilibria.

 

Talk 1 of the contributed session Fri.1.MA 005
"New models and solution concepts II" [...]
Cluster 8
"Game theory" [...]

 

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