I'm reading about Lemke-Howson algorithm from "Algorithmic Game Theory" book, in the exercise part there is question as follow:
Show that the “projection” to polytope P, say, of a LH path from (x, y) to (x',y') in P × Q is also a path in P from x to x'. Hence, if (x, y) is an equilibrium, where can x be on that projected path?
But I don't get what's the purpose of the question, Can someone please just tell me what's the meaning of the question? What does it mean by "Projection to polytope"?