When normal and extensive form decisions differ

Abstract

This chapter reviews the nonequivalence of extensive and normal forms. The “traditional” view of normative decision theory proposes a reduction of sequential decisions problems to nonsequential decisions: a reduction of extensive forms to normal forms. Nonetheless, this reduction is not without its critics, both from inside and outside expected utility theory. Sequential decisions, in extensive form, may lead to different outcomes than their nonsequential, normal form versions, in a variety of problems where the normal form fails to eliminate some “future” options that will not be chosen. The chapter discusses the Harsanyi-Selten argument, applied to Game Theory. They use this thesis to distinguish “perfect” from “imperfect” equilibria in extensive forms and show that this distinction is lost in the reduction to normal forms. They appeal to a “trembling hands” model of players' options to salvage a modified version of the reduction. The chapter also addresses an ingenious argument, due to M. Goldstein, which uses the extensive-normal form reduction to constrain a coherent agent's current beliefs about the future degrees of belief.