A Omitted proofs of Section 3

H . Using these observations we bound the growth function, Π In this proof we consider the notation introduced above in Section B.1. The proof of Theorem 7 will occupy this section. H . (II) For each label null = 2,...,k, there is at most 1 index j [n ] such that h Consider a setting of an iterative game in which a "chooser" player picks a "hidden" We now consider a slight modification of the setting defined above. Next, we are ready to prove the main result, stated in Theorem 7. C.3 Proof of Theorem 7 Proof. (see Definition 1).