Unawareness of theorems

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent's knowledge, but also, can impair his reasoning about what other agents know. For example, in contrast to Li (2006), Heifetz et al. (2006a) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.

A Canonical Model for Interactive Unawareness

Heifetz, Meier and Schipper (2005) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation

Awareness-Dependent Subjective Expected Utility

We develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2011a) as primitives in the Anscombe-Aumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is ``null'' and the negation of the event is ``null''. Moreover, we characterize ``impersonal'' expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness.unawareness, awareness, unforeseen contingencies, null, probability zero, subjective probability, Anscombe-Aumann, small worlds

Revealed Unawareness

I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, I characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. I discuss in what sense impersonal expected utility can not represent unawareness.Unawareness, awareness, unforeseen contingencies, null, zero probability, subjective expected utility, Anscombe-Aumann, small worlds, extensionality of acts, event exchangeability

Revealed Unawareness

I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, I characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. I discuss in what sense impersonal expected utility can not represent unawareness.Unawareness; awareness; unforeseen contingencies; null; zero probability; subjective expected utility; Anscombe-Aumann; small worlds; extensionality of acts; event exchangeability

A Canonical Model for Interactive Unawareness

Heifetz, Meier and Schipper (2005) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation.unawareness, awareness, knowledge, interactive epistemology, modal logic, lack of conception, bounded perception

A Canonical Model for Interactive Unawareness

Heifetz, Meier and Schipper (2005) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation.unawareness; awareness; knowledge; interactive epistemology; modal logic; lack of conception; bounded perception

A Canonical Model for Interactive Unawareness

Heifetz, Meier and Schipper (2005) introduced a generalized state-space model that allows for non-trivial unawareness among several individuals and strong properties of knowledge. We show that this generalized state-space model arises naturally if states consist of maximally consistent sets of formulas in an appropriate logical formulation.unawareness, awareness, knowledge, interactive epistemology, modal logic, lack of conception, bounded perception

Preference-Dependent Unawareness

Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null.Unawareness, awareness, knowledge, preferences, subjective expected utility theory, decision theory, null event

Preference-Based Unawareness

Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null.unawareness, awareness, knowledge, preferences, subjective expected utility theory, decision theory, null event