Conditional dominance in games with unawareness
For game theorists, this provides a formal framework to analyze strategic reasoning in games where players may be unaware of certain actions or game structures.
The paper extends the concepts of extensive-form rationalizability and prudent rationalizability to dynamic games with unawareness by characterizing them via iterated conditional dominance in a generalized normal form. It also shows that iterated admissibility depends on extensive-form structure under unawareness.
Heifetz, Meier, and Schipper (2013) introduced dynamic game with unawareness consisting of a partially ordered set of games in extensive form. Here, we study the normal form of dynamic games with unawareness. The generalized normal form associated with a dynamic game with unawareness consists of a partially ordered set of games in norm form. We use the generalized normal form to characterize extensive-form rationalizability (resp., prudent rationalizability) in dynamic games with unawareness by iterated conditional strict (resp., weak) dominance in the associated generalized normal form. We also show that the analogue to iterated admissibility for dynamic games with unawareness depends on extensive-form structure. This is because under unawareness, a player's information set not only determines which nodes she considers possible but also of which game tree(s) she is aware of.