Revealing Sequential Rationality and Forward Induction

Abstract: Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem by characterizing sequential rationality via the new Conditional B-Dominance. Building on this notion, we introduce Iterative Conditional B-Dominance, which is an iterative elimination procedure that characterizes the implications of forward induction in the class of games under scrutiny and selects the unique backward induction outcome in dynamic ordinal games with perfect information satisfying a genericity condition. Additionally, we show that Iterative Conditional B-Dominance, as a `forward induction reasoning' solution concept, captures: $(i)$ the unique backward induction outcome obtained via sophisticated voting in binary agendas with sequential majority voting; $(ii)$ farsightedness in dynamic ordinal games derived from social environments; $(iii)$ a unique outcome in ordinal Money-Burning Games.