[math-fun] Game question

Consider a game in which two players, A and B, each choose distinct integers by turn. A's object is to maximize the length of the longest A.P. among his selected integers. B's object is to limit the length of A's longest A.P. Show that B cannot prevent A from obtaining an A.P. of length 3. Can B prevent A from obtaining an A.P. of some length N? What is the smallest such N?