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Based on a model where deviations from equilibrium play are assumed to identify irrational players who are characterized by ambiguous set-valued strategies, this paper introduces an equilibrium notion for extensive games with ambiguity averse players that yields a precise interpretation for the counterfactual reasoning usually associated with backward induction. The resulting equilibria are always Nash equilibria, but may not satisfy the conditions required for various refinements of Nash equilibrium, including those for subgame perfection. Existence of such equilibria is proved for all two-player games, and for N -player games with perfect information. [ABSTRACT FROM AUTHOR]

Abstract: Within an epistemic model for two-player extensive games, we formalize the event that each player believes that his opponent chooses rationally at all information sets. Letting this event be common certain belief yields the concept of sequential rationalizability. Adding preference for cautious behavior to this event likewise yields the concept of quasi-perfect rationalizability. These concepts are shown to (a) imply backward induction in generic perfect information games, and (b) be non-equilibrium analogues to sequential and quasi-perfect equilibrium, leading to epistemic characterizations of the latter concepts. Conditional beliefs are described by the novel concept of a system of conditional lexicographic probabilities. [Copyright &y& Elsevier]