The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness Rustichini, 1994, Dekel, Lipman andRustichini, 1998). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies strong properties of knowledge as well as all the desiderata on unawareness proposed this far in the literature. JEL-Classifications: C70, C72, D80, D82.

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized "No-speculative-trade" theorem according to which there cannot be common certainty of strict preference to trade. Moreover, we prove a generalization of the "No-agreeing-to-disagree" theorem.

In an experiment using two-bidder first-price sealed-bid auctions with symmetric independent private values and 400 participants, we collected information on the female participants' menstrual cycles and the use of hormonal contraceptives. We find that naturally cycling women bid significantly higher than men and earn significantly lower profits than men except during the midcycle when fecundity is highest. We suggest an evolutionary hypothesis according to which women are predisposed by hormones to generally behave more riskily during their fecund phase of their menstrual cycle in order to increase the probability of conception, quality of offspring, and genetic variety. We also find that women on hormonal contraceptives bid significantly higher and earn substantially lower profits than men. This may be due to progestins contained in hormonal contraceptives or a selection effect. We discuss how our study differs from Chen, Katuščák, and Ozdenoren (2012).

Heifetz, Meier and Schipper (2006) introduced unawareness structures. These are generalized state-space models that allow for non-trivial unawareness among several individuals and strong properties of knowledge. We show that a canonical unawareness structure arises naturally if states consist of maximally consistent sets of formulas in an appropriate axiom system. As a corollary, we obtain a strong soundness and completeness theorem for this axiom system with respect to the class of unawareness structures.

We define generalized extensive-form games which allow for asymmetric awareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties, and prove existence.