A utility function is called GS if, according to this utility function, all pairs of different goods are GS. With a GS utility function, if an agent has a demand set at a given price vector, and the prices of some items increase, then the agent has a demand set which includes all the items whose price remained constant. He may decide that he doesn't want an item which has become more expensive; he may also decide that he wants another item instead (a substitute); but he may not decide that he doesn't want a third item whose price hasn't changed.