  In this paper, we consider the {\it generalized polynomial complementarity
problem} (GPCP), which covers the recently introduced {\it polynomial
complementarity problem} (PCP) and the well studied {\it tensor complementarity
problem} (TCP) as special cases. By exploiting the structure of tensors, we
first show that the solution set of GPCPs is nonempty and compact when a pair
of leading tensors is cone {\bf ER}. Then, we study some topological properties
of the solution set of GPCPs under the condition that the leading tensor pair
is cone ${\bf R}_0$. Finally, we study a notable global Lipschitzian error
bound of the solution set of GPCPs, which is better than the results obtained
in the current PCPs and TCPs literature. Moreover, such an error bound is
potentially helpful for finding and analyzing numerical solutions to the
problem under consideration.
