Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2008-011 (October 15, 2008)
Parametrized Variational Inequality Approaches to Generalized Nash Equilibrium Problems with Shared Constraints
by Koichi Nabetani, Paul Tseng and Masao Fukushima
We consider the generalized Nash equilibrium problem (GNEP),
in which each player's strategy set may depend on the rivals'
strategies through shared constraints.
A practical approach to solving this problem that has received
increasing attention lately entails solving a related variational
From the viewpoint of game theory, it is important to find
as many GNEs as possible, if not all of them.
We propose two types
of parametrized VIs related to the GNEP, one price-directed and
the other resource-directed. We show that these parametrized VIs
inherit the monotonicity properties of the original VI and,
under mild constraint qualifications, their solutions yield all GNEs.
We propose strategies to sample in the parameter spaces and
show, through numerical experiments on benchmark examples,
that the GNEs found by the parametrized VI approaches are widely
distributed over the GNE set.