Sequential Rationality and Ordinal Preferences

Abstract

Given a dynamic game with ordinal preferences, we deem a strategy sequentially rational if there exist a von Neumann-Morgenstern utility function that agrees with the assumed ordinal preferences and a conditional probability system with respect to which the strategy is a maximizer. We prove that this notion of sequential rationality is characterized by a notion of dominance, called Conditional B-Dominance, that extends Pure Strategy Dominance of Börgers (1993) to dynamic games represented in their extensive form. Additionally, we introduce an iterative procedure based on Conditional B-Dominance with a forward induction reasoning flavour, called Iterative Conditional B-Dominance, that we prove: (i) satisfies nonemptiness; (ii) algorithmically characterizes an ‘ordinal’ version of Strong Rationalizability à la Pearce (1984) and Battigalli (1997); (iii) selects the unique backward induction outcome in dynamic games with perfect information that satisfy the genericity condition called “No Relevant Ties”. Finally, we show how our results on Iterative Conditional B-Dominance allow a ‘forward induction reasoning’ interpretation of the unique backward induction outcome obtained in binary agendas with sequential majority voting.

Keywords: Dynamic Games, Ordinal Preferences, Sequential Rationality, Forward Induction, Conditional Pure Strategy/Börgers Dominance, Iterative Conditional B-Dominance

JEL Classification: C63, C72, C73