Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2008-007 (July 31, 2008)
Restricted Generalized Nash Equilibria and Controlled Penalty Algorithm
by Masao Fukushima
The generalized Nash equilibrium problem (GNEP) is a generalization
of the standard Nash equilibrium problem (NEP), in which each player's
strategy set may depend on the rival players' strategies.
The GNEP has recently drawn much attention because of its
capability of modeling a number of interesting conflict situations in,
for example, an electricity market and an international pollution control.
However, a GNEP usually has multiple or even infinitely many solutions,
and it is not a trivial matter to choose a meaningful solution from those
equilibria. The purpose of this paper is two-fold.
First we present an incremental penalty method for the broad class of
GNEPs and show that it can find a GNE under suitable conditions.
Next, we formally define the restricted GNE for the GNEPs with
shared constraints and propose a controlled penalty method,
which includes the incremental penalty method as a subprocedure,
to compute a restricted GNE.
Numerical examples are provided to illustrate the proposed approach.