# Standard state-space models preclude unawareness

@article{Dekel1998StandardSM, title={Standard state-space models preclude unawareness}, author={Eddie Dekel and Barton L. Lipman and Aldo Rustichini}, journal={Econometrica}, year={1998}, volume={66}, pages={159-173} }

We show that a very broad class of models, including possibility correspondences, necessarily fail to capture very simple and intuitive implications of unawareness. We explain why standard state–space formulations suffer from this problem, illustrating the point with an example of a nonstandard state–space model which avoids the difficulty.

## 270 Citations

### A canonical model for interactive unawareness

- MathematicsTARK '07
- 2007

It is shown that a canonical unawareness structure arises naturally if states consist of maximally consistent sets of formulas in an appropriate axiom system and as a corollary, a strong soundness and completeness theorem is obtained.

### Multi-person unawareness

- EconomicsTARK '03
- 2003

A generalized state-space model that allows for unawareness is defined that satisfies all "S4" properties as well as all desiderata on unawareness proposed by Modica and Rustichini (1999) and Halpern (2001).

### We define a generalized state-space model with interactive unawareness and probabilistic beliefs . Such models are desirable for potential applications of asymmetric unawareness

- Economics
- 2011

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…

### Sub-models for interactive unawareness

- Economics
- 2015

This work proposes a notion of a sub-model for each agent at each state in the Heifetz et al. (2006) model of interactive unawareness and uses sub-models to motivate the HMS conditions on possibility correspondences.

### Modelilng Unawareness in Arbitrary State Spaces

- Economics
- 2008

I develop a set-theoretic model of unawareness without making any structural assumptions on the underlying state space. Unawareness is characterized as a measurability constraint that results in…

### TITLE : Sub-models for Interactive Unawareness

- Economics
- 2014

We propose a notion of a sub-model for each agent at each state in the Heifetz et al (2006) model of interactive unawareness. Presuming that each agent is fully cognizant of his sub-model causes no…

### Information Structures with Unawareness

- Computer ScienceJ. Econ. Theory
- 2009

A model that circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem.

### Unawareness, Beliefs, and Speculative Trade

- EconomicsGames Econ. Behav.
- 2013

A generalized "No-speculative-trade" theorem is proved according to which there can not be common certainty of strict preference to trade and the existence of a universal unawareness belief type space is shown.

### Standard State Space Models of Unawareness (Extended Abstract)

- PhilosophyTARK
- 2015

This work distinguishes three notions of awareness, and argues that although one of them may not be adequately modeled using standard state spaces, there is no reason to think thatstandard state spaces cannot provide models of the other two notions.

### Unawareness, beliefs and games

- EconomicsTARK '07
- 2007

A generalized " no-trade" theorem is proved according to which there can not be common certainty of strict preference to trade and a generalization of the "No-agreeing-to-disagree"orem is shown.

## References

SHOWING 1-10 OF 20 REFERENCES

### Logical Structure of Common Knowledge

- Economics
- 1993

Abstract When " i knows p " is defined as " i can prove p ," information takes the form of a topology on a propositional state space. This allows a simple characterization of common knowledge. It…

### The Logic of Belief and Belief Change: A Decision Theoretic Approach

- Economics
- 1996

Savage [L. Savage, ‘‘The Foundations of Statistics,’’ Wiley, New York, 1954] showed how properties of a decision maker’s probabilistic beliefs can be deduced from primitive consistency axioms on…

### Awareness and partitional information structures

- Economics, Philosophy
- 1994

This is the first of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows that thing; he…

### Unawareness: A Formal Theory of Unforeseen Contingencies. Part I

- Economics, Philosophy
- 1993

This is the first of a sequence of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows…

### Modal Logic - An Introduction

- Philosophy
- 1980

This chapter discusses standard models for modal logics, classical systems of modal logic, and Determination and decidability for classical systems.

### Reasoning about knowledge

- Computer Science
- 1995

Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory.