Unawareness, Beliefs, and Speculative Trade

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 can not be common certainty of strict preference to trade. Moreover, we prove a generalization of the "No-agreeing-to-disagree" theorem. Finally, we show the existence of a universal unawareness belief type space.Unawareness, awareness, common prior, agreement, speculative trade, universal type-space, interactive epistemology, inattention

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

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.

Awareness in Repeated Games

In this paper we provide a framework to reason about limited awareness of the action space in finitely repeated games. Our framework is rich enough to capture the full strategic aspect of limited awareness in a dynamic setting, taking into account the possibility that agents might want to reveal or conceal actions to their opponent or that they might become "aware of unawareness" upon observing non rationalizable behavior. We show that one can think of these situations as a game with incomplete information, which is fundamentally different, though, from the standard treatment of repeated games with incomplete information. We establish conditions on the "level of mutual awareness" of the action space needed to recover Nash and subgame perfect Nash equilibria from the standard theory with common knowledge. We also show that the set of sustainable payoffs in games with folk theorems does not relate in a monotone way to the "level of mutual awareness".mathematical economics;

A reasoning approach to introspection and unawareness

We introduce and study a unified reasoning process which allows to represent the beliefs of both a fully rational agent and of an unaware one. This reasoning process provides natural properties to introspection and unawareness. The corresponding model for the rational or boundedly rational agents is both easy to describe and to work with, and the agent’s full system of beliefs has natural descriptions using a reduced number of parameters.Economics (Jel: A)

Stepwise Thinking in Strategic Games with Incomplete Information

This paper proposes a general incomplete information framework for studying behavior in strategic games with stepwise (viz. `level-k' or `cognitive hierarchy') thinking, which has been found to describe strategic behavior well in experiments involving players' initial responses to games. It is shown that there exist coherent stepwise beliefs, implied by step types, that have the potential to encode all relevant information. In the structure of stepwise beliefs, players are unaware of opponents doing at least as much thinking as themselves. As a result, there exists a Bayesian Nash equilibrium strategy profile in which any player at some step fixes the best responses of opponents at lower steps and then best responds herself.game theory; interactive epistemology; unawareness; Bayesian Nash equilibrium; bounded rationality; level-k; cognitive hierarchy

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

Unawareness, Beliefs and Speculative Trade

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-to-disagree"" theorem.unawareness, awareness, zero probability, type-space, common prior, agreement, speculative trade, interactive epistemology

Unawareness, Beliefs and Games

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We use our unawareness belief structure to 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-to-disagree'' theorem.unawareness, awareness, type-space, Bayesian games, incomplete information, equilibrium, common prior, agreement, speculative trade, interactive epistemology

Unawareness, Beliefs and Games

We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We use our unawareness belief structure to 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-to-disagree†theorem.unawareness; awareness; type-space; Bayesian games; incomplete information; equilibrium; common prior; agreement; speculative trade; interactive epistemology