Pure Backward Induction Reasoning in Dynamic Games (2025)

EPICENTER Working Paper No. 34

Abstract: Properties BI1 and BI2 in Kohlberg and Mertens (1986) entail that the solution of a dynamic game, when restricted to a subgame, should yield the same as applying the solution to the subgame in isolation. Remarkably, none of the existing equilibrium and rationalizability concepts satisfies this pure backward induction principle. This paper offers a action-based rationalizability concept that does. It is based on the epistemic condition that a player, at every history, believes that his opponents', and he himself, will choose optimal actions in the future. Iterating this condition leads to common belief in future action-based rationality. Its behavioral consequences are characterized by a computationally convenient elimination procedure, called the double-utility procedure. In perfect information games it yields backward induction, whereas it simplifies to a very easy procedure in finitely repeated games.

Forward induction in a backward inductive manner (2025)

with Martin Meier

Abstract: We propose a new rationalizability concept for dynamic games with imperfect information, forward and backward rationalizability, that combines elements from forward and backward induction reasoning. It proceeds by applying the forward induction concept of strong rationalizability (also known as extensive-form rationalizability) in a backward inductive fashion. We argue that, compared to strong rationalizability, the new concept provides a more compelling theory for how players react to surprises. Moreover, we provide an epistemic characterization of the new concept, and show that (a) it always exists, (b) in terms of outcomes it is equivalent to strong rationalizability, (c) in terms of strategies it is a refinement of the pure backward induction concepts of backward dominance and backwards rationalizability, and (d) it satisfies expansion monotonicity: if a player learns that the game was actually preceded by some moves he was initially unaware of, then this new information will only refine, but never completely overthrow, his reasoning. Strong rationalizability violates this principle.

More reasoning, less outcomes: A monotonicity result for reasoning in dynamic games (2025)

Online appendix

EPICENTER Working Paper No. 32

Abstract: A focus function in a dynamic game describes, for every player and each of his information sets, the collection of opponents' information sets he reasons about. Every focus function induces a rationalizability procedure in which a player believes, whenever possible, that his opponents choose rationally at those information sets he reasons about. Under certain conditions, we show that if the players start reasoning about more information sets, then the set of outcomes induced by the associated rationalizability procedure becomes smaller or stays the same. This result does not hold on the level of strategies, unless the players only reason about present and future information sets. The monotonicity result enables us to derive existing theorems, such as the relation in terms of outcomes between forward and backward induction reasoning, but also paves the way for new results.