Agnostic Sequential Rationality

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An agnostic sequential equilibrium is a refinement of sequential equilibrium that does not force on the players a single, arbitrary beliefs system. In fact, a strategy profile in an extensive-form game with perfect recall is an ASE if and only if it is sequential equilibrium with every fully consistent belief system. However, ASE is not defined in terms of full consistency (which uses perturbations of strategies) but is based on a simpler, novel notion of consistency between strategy profiles and off-equilibrium beliefs that is applicable to a large class of dynamic games, including games with a continuum of actions. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players’ actions unspecified in some, or many, information sets.

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