Discovery Process in Normal-Form Games with Unawareness: Cognitive Stability and Closedness under Rational Behavior

This study examines how each player chooses her/his optimal action in "normal-form games with unawareness" by applying a "discovery process" to them. We show that if each player implements a best response to the opponents' immediately preceding plays, then any discovery process converges to a set closed under rational behavior (CURB) on the realizable action set. Moreover, in the objective game in any initial normal-form game with unawareness, when every CURB set on the realizable action set is mutually known, every discovery process converges to a discovered game possessing a cognitively stable generalized Nash equilibrium. It is not necessary that each player must be aware of the opponents' utilities in our results.