%Federica Tinti (ftinti@math.unipd.it)
%Department of Mathematics of Ferrara (ITALY)
%
%map of Pang & Murphy's Nash-Cournot test problem
%
function [f]=PMnashc5(x)
%
%test problem NASH-COURNOT    n=5 
%
%Reference:
%J.-S. Pang, S.A. Gabriel, 'NE/SQP: A robust algorithm for the nonlinear 
%complementarity problem', Mathematical Programming, 60 (1993), pp.295-337.
%
%F.H. Murphy, H.D. Sherali, A.L. Soyster, 'A mathematical programming 
%approach for determining oligopolistic market equilibrium', 
%Mathematical Programming, 24 (1982), pp. 92-106.
%
c=[10 8 6 4 2]';
b1=[1.2 1.10 1 0.9 0.8]';
L=5*ones(5,1);
gamma=1.1;
gamma1=1./gamma;
temp=sum(x);
aux=1./b1; 
f=c+L.^(-aux).*x.^(aux)-(5000/temp).^(gamma1)*(ones(size(x))-gamma1*x/temp);