We generalize the “No-trade ” theorem for finite unawareness belief structures in Heifetz, Meier, and Schipper (2009) to the infinite case.

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. (2006) 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.

In earlier work [Halpern and Rêgo 2006b], we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern [1988] by

A central theme in behavioral economics focuses on experimental evidence that individuals learn from the choice problems they face and consequently violate the consistency requirements of revealed preference theory. Despite the experimental evidence, the testable implications of such contextual inference remain unclear. In particular, it is an open question if learning from the choice problem imposes any restrictions on observed behavior. Motivated by the Shafir and Tversky [18] experiments, this paper models contextual inference in the framework of preference for flexibility introduced by Kreps [10] and extended by Dekel, Lipman, and Rustichini [4]. Within this framework, the paper proposes a relaxation of the weak axiom which formalizes the identification strategy in Shafir and Tversky [18]. A subjective state space that may depend on the subset of actions faced by the individual is uniquely identified from behavior, and local preferences are partially recovered.

Abstract not found

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. 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-trade ” theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the “No-agreeing-todisagree” theorem.

We provide a complete and sound axiomatization of the set-theoretic model of Galanis [2007a]. By constructing a syntax with several knowledge modalities, one for each sub-language, we are able to allow for agents to make mistakes about the knowledge of others without discarding the truth axiom. Comparing the present axiom system with that of Heifetz et al. [2008a] we find that neither is a generalization of the other. 1

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.

We 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. 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.

We provide a tool to model and solve strategic situations where players reasoning is limited, in the sense that they may only be aware of, or model, some of the aspects of the strategic situations at hand, as well as situations where players realize that other players ’ perceptions may be limited. We define normal, repeated, incomplete information, and dynamic (extensive) form games with unawareness using a unified methodology. A game with unawareness is defined as a collection of standard games (of the corresponding form. The collection specifies how each player views the game, how she views the other players ’ perceptions of the game and so on. The modeler’s description of perceptions, the players ’ description of other players ’ reasoning, etc. are shown to have consistent representations. We extend solution concepts such as rationalizability and Nash equilibrium to these games and study their properties. It is shown that while unawareness in normal form games can be mapped to incomplete information games, the extended Nash equilibrium is not mapped to a known solution concept in incomplete information games, implying that games with unawareness generate novel types of behavior. JEL Classification: C72,D81,D82. 1