Agnostic Sequential Rationality

Igal Milchtaich

Abstract

Agnostic sequential equilibrium is a refinement of sequential equilibrium that does not force on the players a single, arbitrary belief system. In fact, a strategy profile in an imperfect-information extensive-form game with perfect recall is an ASE if and only if it is a sequential equilibrium with every fully consistent belief system. However, ASE is not defined in terms of full consistency (which employs perturbations of strategies) but is based on a simpler, 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 this, the new solution concept is similar to perfect Bayesian equilibrium. ASE is generalized by the set-valued solution concept of agnostic sequential polyequilibrium, which allows leaving the players’ actions in some (possibly, most) information sets partially or completely unspecified.

JEL classification

C72

Keywords

Agnostic sequential equilibrium; Agnostic sequential polyequilibrium; Strong consistency; Perfect Bayesian equilibrium