Agnostic Sequential Rationality
TL;DR
It is shown that a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE precisely when it is a sequential equilibrium with every fully consistent belief system.
Abstract
Agnostic sequential equilibrium (ASE) is a refinement of sequential equilibrium that does not force on the players a single, arbitrary belief system. In addition, whereas sequential equilibrium assumes the players'beliefs to be fully consistent (a notion that is based on perturbations of strategies), ASE employs a novel, simpler and local concept of strong consistency between strategy profiles and off-equilibrium beliefs, which is applicable to a large class of dynamic games, including games with a continuum of actions. In the last respect, the new solution concept is similar to perfect Bayesian equilibrium. It is shown that a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE precisely when it is a sequential equilibrium with every fully consistent belief system. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players'actions in some information sets partially or completely unspecified.