Generalised Solution Concepts in Games without Expected Utility (2025)

with Ákos Balázs

EPICENTER Working paper No. 35

Abstract: We propose a general framework for strategic interaction that relaxes the expected utility assumption and instead works directly with players’ conditional preference relations (Gilboa & Schmeidler, 2003; Perea, 2025). By leveraging their epistemic foundations, we show that three classical solution concepts admit natural generalisations to this broader setting without altering their underlying reasoning principles. First, we introduce the iterated elimination of never-optimal choices as an analogue of the iterated elimination of strictly dominated choices, characterised by common belief in rationality. We also prove that it always yields a non-empty solution. Second, we generalise Nash equilibrium, preserving its characterisation by common belief in rationality and simple beliefs. Third, we extend correlated equilibrium, characterised by common belief in rationality and a common prior. While the latter two solution concepts are not guaranteed to exist in all games, we identify a sufficient condition for their existence, which we call strong continuity. This property requires the set of beliefs where a choice is weakly preferred to another to be closed, for any player and any choice pair. We also show that this condition is equivalent to imposing a continuous utility representation on the game, but weaker than imposing an expected utility representation. Our results demonstrate that the foundations of game theory are robust to the relaxation of expected utility, opening the door to richer and more flexible models of strategic interaction.

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.