On the Equivalence of Normal and Extensive Form Representations of Games

Abstract

AbstractIn this chapter I examine the traditional position in game theory concerning the adequacy of the normal form representations of extensive form games. According to this traditional view, an extensive form game can be reduced to a normal form game without loss of strategically relevant information about the structure of the game. Many game theorists have already raised questions about such a reduction from a game in extensive form to strategic form by considering solution concepts that explicitly use the extensive form structure of the game. In the same vein, I evaluate the traditional view of the equivalence of extensive and normal form games in a systematic way. Within the traditional game-theoretic framework, I show that two extensive form games with the same reduced normal form may lead to different outcomes, and thus are not strategically equivalent. In addition, I demonstrate that the reduced normal form of an extensive form game cannot sufficiently represent certain reasonable strategic reasoning in the game of extensive form.