1,721,127 research outputs found
Epistemic foundations for set-algebraic representations of knowledge
No full textThis paper formalizes an informal idea that an agent’s knowledge is characterized by a collection of sets such as a sigma-algebra within the framework of a state space model. The paper fully characterizes why the agent’s knowledge takes (or does not take) such a set algebra as a sigma-algebra or a topology, depending on logical and introspective properties of knowledge and on the underlying structure of the state space. The agent’s knowledge is summarized by a collection of events if and only if she can only know what is true, she knows any logical implication of what she knows, and she is introspective about what she knows. In this case, for any event, the collection that represents knowledge has the maximal event included in the original event. When the underlying space is a measurable space, the collection becomes a sigma-algebra if and only if the agent is additionally introspective about what she does not know
On the axiomatization of an unawareness structure from knowing-whether operators
No full textThis paper shows that, on a generalized state space model of unawareness, an agent’s underlying knowledge is axiomatized from her knowing-whether operator if and only if her knowledge satisfies the Truth Axiom: whenever the agent knows an event, the event holds. The agent knows whether an event obtains if she knows it or knows its negation. Different knowledge operators lead to different knowing-whether operators if knowledge is truthful. Conversely, for any knowing-whether operator, there is a unique truthful knowledge operator that induces the given knowing-whether operator: the agent knows an event if and only if she knows whether the event holds and the event indeed holds. Qualitative or probabilistic beliefs may not be recovered from believing-whether. This paper then axiomatizes properties of knowledge and common knowledge, in terms of knowing-whether. The main contributions of the paper are as follows. First, conceptually, this paper provides a generalized-state-space model of knowledge and unawareness in which the only assumption on knowledge is the Truth Axiom. Second, practically, this paper may provide a simple way to construct a generalized-state-space model
The existence of universal qualitative belief spaces
No full textThis paper constructs a canonical representation of players’ interactive beliefs, irrespective of natures of beliefs: whether beliefs are qualitative, truthful (i.e., knowledge), or probabilistic (e.g., countably-additive, finitely-additive, or non-additive). The canonical model is the “largest” interactive belief model to which any particular model can be mapped in a unique belief-preserving way. The key insight for the construction is the need to specify players’ possible depth of reasoning up to which they can interactively reason about their beliefs (e.g., their beliefs, their beliefs about their beliefs, their beliefs about their beliefs about their beliefs, and so on). The possible depth of reasoning may be a transfinite level (beyond any finite level) when beliefs are qualitative. The specification of possible depth of reasoning also has game-theoretic
implications for characterizations of some solution concepts using the canonical
space. For instance, for any strategic game with ordinal payoffs, there exists
a canonical interactive belief model which characterizes iterated elimination of
strictly dominated actions as an implication of common belief in rationality
On the consistency among prior, posteriors, and information sets
No full textThis paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. The main implication of this result is to provide a tractable epistemic model which dispenses with the technical assumptions inherent in the standard epistemic model such as the
countable number of information sets. Applications are agreement theorem, no-trade theorem, and the epistemic characterization of correlated equilibria. Implications are as follows. First, since qualitative belief reduces to fully introspective knowledge in the standard environment, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Second, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Third, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs
On the consistency among prior, posteriors, and information sets (Extended Abstract)
No full textNo abstract availabl
Unawareness without AU Introspection
No full textThis paper studies unawareness in terms of the lack of knowledge in a model that generalizes both a non-partitional standard-state-space model and a stationary generalized-state-space model. The resulting model may not necessarily satisfy AU Introspection: an agent, who is unaware of an event, is unaware of being unaware of it. Yet, the paper shows that such agent does not know whether she is unaware of it, i.e., she is ignorant of being unaware of it. First, the paper asks when and how the generalized model (in particular, a standard-state-space model) has a non-trivial form of unawareness and sensible properties of unawareness. Second, the paper studies the implications of the violation of AU Introspection. An agent, when facing infinitely many objects of knowledge, may know that there is an event of which she is unaware. Treating new information only at face value can cause an agent to become unaware of some event
Formalizing common belief with no underlying assumption on individual beliefs
No full textThis paper formalizes common belief among players with no underlying assumption on their individual beliefs. Especially, players may not be logically omniscient, i.e., they may not believe logical consequences of their beliefs. The key idea is to use a novel concept of a common basis: it is an event such that, whenever it is true, every player believes its logical consequences. The common belief in an event obtains when a common basis implies the mutual belief in that event. If players' beliefs are assumed to be true, then common belief reduces to common knowledge. The formalization nests previous axiomatizations of common belief and common knowledge which have assumed players' logical monotonic reasoning. Under this formalization, unlike others, if players have common belief in rationality then their actions survive iterated elimination of strictly dominated actions even if their beliefs are not monotonic
Negotiations with limited specifiability
No full textWe study negotiations withlimited specifiability—each party may not beable to fully specify a negotiation outcome. We construct a class of negotiation protocols to conduct comparative statics on specifiability as well as move structures. We find that asynchronicity of proposal announcements narrows down the equilibrium payoff set, in particular leading to a unique prediction in negotiations with a ``common interest'' alternative. The equilibrium payoff set is not a singleton in general, and depends on the fine details of how limitation on specifiability is imposed. The equilibrium payoff set is weakly larger under limited specifiability than under unlimited specifiability
Epidemics with behavior
No full textWe study social distancing in an epidemiological model. Distancing reduces the individual's probability of getting infected but comes at a cost. Equilibrium distancing flattens the curve and decreases the final size of the epidemic. We examine the effects of distancing on the outset, the peak, and the final size of the epidemic. First, the prevalence increases beyond the initial value only if the transmission rate is in the intermediate region. Second, the peak of the epidemic is non-monotonic in the transmission rate. A reduction in the transmission rate can increase the peak. However, a decrease in the cost of distancing always flattens the curve. Third, both a reduction in the transmission rate as well as a reduction in the cost of distancing decrease the final size of the epidemic. Our results suggest that public policies that decrease the transmission rate can lead to unintended negative consequences in the short run but not in the long run. Therefore, it is important to distinguish between interventions that affect the transmission rate and interventions that affect contact rates
- …
