Ability and knowledge

In games with incomplete information, more information to a player implies a broader strategy set for this player in the normal form game, hence more knowledge implies more ability. We prove that, conversely, given two normal form games G and G′ such that players in a subset J of the set of players possess more strategies in G′ than in G, there exist two games with incomplete information with normal forms G and G′ such that players in J are more informed in the second than in the first. More ability can then be rationalized by more knowledge, and our result thus establishes the formal equivalence between ability and knowledge.