The $n$-sector $(n\geq2)$ open-loop Nash strategies 
can not be discussed directly within the framework 
of usual variational principle. In this paper, 
by extending the original variables, it is shown 
that a maximizing problem under constraints in the 
strategies can be included in a problem (composite 
maximizing problem) in the usual variational principle. 
A model is given for the derivation of conservation laws, 
through which optimal paths are determined completely 
for finite horizon and then detailed for infinite horizon.