1,483 research outputs found
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
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
An epistemic model of an agent who does not reflect on reasoning processes
This paper introduces an epistemic model of a boundedly rational agent under the two assumptions that (i) the agent's reasoning process is in accordance with the model but (ii) the agent does not reflect on these reasoning processes. For such a concept of bounded rationality a semantic interpretation by the possible world semantics of the Kripke (1963) type is no longer available because the definition of knowledge in these possible world semantics implies that the agent knows all valid statements of the model. Key to my alternative semantic approach is the extension of the method of truth tables, first introduced for the propositional logic by Wittgenstein (1922), to an epistemic logic so that I can determine the truth value of epistemic statements for all relevant truth conditions. I also define an axiom system plus inference rules for knowledge- and unawareness statements whereby I drop the inference rule of necessitation, which claims that an agent knows all theorems of the logic. As my main formal result I derive a determination theorem linking my semantic with my syntactic approach.Bounded Rationality, Knowledge, Unawareness, Epistemic Logic, Semantic Interpretation, Iterative Solution Concepts for Strategic Games
Extensive Games with Possibly Unaware Players
Standard game theory assumes that the structure of the game is common
knowledge among players. We relax this assumption by considering extensive
games where agents may be unaware of the complete structure of the game. In
particular, they may not be aware of moves that they and other agents can make.
We show how such games can be represented; the key idea is to describe the game
from the point of view of every agent at every node of the game tree. We
provide a generalization of Nash equilibrium and show that every game with
awareness has a generalized Nash equilibrium. Finally, we extend these results
to games with awareness of unawareness, where a player i may be aware that a
player j can make moves that i is not aware of, and to subjective games, where
payers may have no common knowledge regarding the actual game and their beliefs
are incompatible with a common prior.Comment: 45 pages, 3 figures, a preliminary version was presented at AAMAS0
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
Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model
Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The
HMS model is syntax-free, which precludes the simple option to rely on formal
language to induce lattices, and represents uncertainty and unawareness with
one entangled construct, making it difficult to assess the properties of
either. Here, we present a model based on a lattice of Kripke models, induced
by atom subset inclusion, in which uncertainty and unawareness are separate. We
show the models to be equivalent by defining transformations between them which
preserve formula satisfaction, and obtain completeness through our and HMS'
results.Comment: 18 pages, 2 figures, proceedings of DaLi conference 202
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
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