Normal Form Structures in Extensive Form Games

Mailaith, Samuelson, and Swinkels (1992) introduce the normal form information set. 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 situation, the corresponding choice in the extnesive form is made with the player knowing that the opponents have chosen from the relevant subset. We show that normal form games exist that cannot be represented. 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. Keywords: representation, extensive form game, normal form game, information set, extensive form--normal form equivalence. JEL Classification Numbers: C70, C72.