Interactive Unawareness Revisited

We analyze a model of interactive unawareness introduced by Heifetz, Meier and Schipper (HMS). We consider two axiomatizations for their model, which capture different notions of validity. These axiomatizations allow us to compare the HMS approach to both the standard (S5) epistemic logic and two other approaches to unawareness: that of Fagin and Halpern and that of Modica and Rustichini. We show that the differences between the HMS approach and the others are mainly due to the notion of validity used and the fact that the HMS is based on a 3-valued propositional logic.Comment: 26 page

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 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.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

Standard State Space Models of Unawareness

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly

Decision Making with Imperfect Knowledge of the State Space

We conduct an experiment to study how imperfect knowledge of the state space affects subsequent choices under uncertainty with perfect knowledge of the state space. Participants in our experiment choose between a sure outcome and a lottery in 32 periods. All treatments are exactly identical in periods 17 to 32 but differ in periods 1 to 16. In the early periods of the “Risk Treatment” there is perfect information about the lottery; in the “Ambiguity Treatment” participants perfectly know the outcome space but not the associated probabilities; in the “Unawareness Treatment” participants have imperfect knowledge about both outcomes and probabilities. All three treatments induce strong behavioural differences in periods 17 to 32. In particular participants who have been exposed to an environment with very imperfect knowledge of the state space subsequently choose lotteries with high (low) variance less (more) often compared to other participants. Estimating individual risk attitudes from choices in periods 17 to 32 we find that the distribution of risk attitude parameters across our treatments can be ranked in terms of first order stochastic dominance. Our results show how exposure to different degrees of uncertainty can have long-lasting effects on individuals’ risk-taking behaviour.microeconomics ;

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