Department of Applied Mathematics & Physics, Kyoto University
Technical Report 2011-004 (January 27, 2011)
Smoothing Approach to Nash Equilibrium Formulations for a Class of Equilibrium Problems with Shared Complementarity Constraints
by Ming Hu and Masao Fukushima
The equilibrium problem with equilibrium constraints
(EPEC) can be looked on as a generalization of Nash
equilibrium problem (NEP) and the mathematical program
with equilibrium constraints (MPEC) whose
constraints contain a parametric variational inequality
or complementarity system. In this paper,
we particularly consider a special class of EPECs
where a common parametric P-matrix linear complementarity
system is contained in all players' strategy sets.
After reformulating the EPEC as an equivalent NEP, we use
a smoothing method to construct a sequence of smoothed
NEPs that approximate the original problem.
We consider two solution concepts, global Nash
equilibrium and stationary Nash equilibrium,
and establish some results about the convergence
of approximate Nash equilibria.