Normal Form Structures in Extensive Form Games

Normal form information sets capture situations in which players can make certain decisions as if they knew their opponents had chosen from a particular subset of their strategies. In this paper, we say that an extensive form game represents a normal form game if, for each such situation, the corresponding choice in the extensive form is made with the player knowing that the opponents have chosen from the relevant subset. We develop an algorithm that generates a representation whenever one exists and present a necessary and sufficient condition for a normal form game to be representable.