1,356,002 research outputs found
Syntactic foundations for unawareness of theorems
No full textWe provide a syntactic model of unawareness. By introducing multiple knowledge modalities, one for each sub-language, we specifically model agents whose only mistake in reasoning (other than their unawareness) is to underestimate the knowledge of more aware agents. We show that the model is a complete and sound axiomatization of the set-theoretic model of Galanis [2007] and compare it with other unawareness models in the literature
Trade and the value of information under unawareness
No full textThe value of information and the possibility of speculation are examined in an environment with unawareness. Although agents have “correct” prior beliefs about events they are aware of and have a clear understanding of their available actions and payoffs, their unawareness may lead them to commit information processing errors and to behave suboptimally. As a result, more information is not always valuable and agents can speculate with each other. We identify two specific information processing errors that are responsible for both problems. Moreover, we construct a dynamic model where agents announce their posteriors and update their awareness as soon as they hear a counterfactual announcement. We study how awareness is updated and whether agreement about posteriors is reached
Approximating Observables Is as Hard as Counting
No full textWe study the computational complexity of estimating local observables for Gibbs distributions. A simple combinatorial example is the average size of an independent set in a graph. A recent work of Galanis et al (2021) established NP-hardness of approximating the average size of an independent set utilizing hardness of the corresponding optimization problem and the related phase transition behavior. We instead consider settings where the underlying optimization problem is easily solvable. Our main contribution is to classify the complexity of approximating a wide class of observables via a generic reduction from approximate counting to the problem of estimating local observables. The key idea is to use the observables to interpolate the counting problem.
Using this new approach, we are able to study observables on bipartite graphs where the underlying optimization problem is easy but the counting problem is believed to be hard. The most-well studied class of graphs that was excluded from previous hardness results were bipartite graphs. We establish hardness for estimating the average size of the independent set in bipartite graphs of maximum degree 6; more generally, we show tight hardness results for general vertex-edge observables for antiferromagnetic 2-spin systems on bipartite graphs. Our techniques go beyond 2-spin systems, and for the ferromagnetic Potts model we establish hardness of approximating the number of monochromatic edges in the same region as known hardness of approximate counting results
The value of information in risk-sharing environments with unawareness
No full textThe value of information is examined in a risk-sharing environment with unawareness and complete markets. Information and awareness are symmetric among agents, who have a clear understanding of their actions and deterministic payoffs. We show with examples that public information can make some agents strictly better off at the expense of others, contrasting the standard results of Hirshleifer [1971] and Schlee [2001] that the value of public information is negative for all when risk averse agents are fully insured. We identify the source of this problem to be that, as awareness varies across states, it creates an “awareness signal” that the agents misunderstand and treat asymmetrically. As a result, risk-sharing opportunities that are available when this signal is not used, vanish when it is used. Depending on the allocation of endowments, this asymmetry makes some agents strictly better off and others strictly worse off. We identify a property, Conditional Independence, which we show is sufficient for the value of public information to be negative for all
The value of information under unawareness
No full textThe value of information is examined in a single-agent environment with unawareness. Although the agent has a correct prior about events he is aware of and has a clear understanding of his available actions and payoffs, his unawareness may lead him to commit information processing errors and to behave suboptimally. As a result, the value of information can be negative, contrasting what is true in the standard model with partitional information and no unawareness. We show that the source of the agent’s suboptimal behavior is that he misunderstands the information revealed by his varying awareness, treating it asymmetrically
Correction: The Role of Attachment Styles on Quality of Life and Distress Among Early-Stage Female Breast Cancer Patients: A Systematic Review (Journal of Clinical Psychology in Medical Settings, (2023), 10.1007/s10880-023-09940-w)
No full textDue to an oversight by this article’s authors, the orders of authors’ first and last names are given incorrectly in the original publication. The authors’ names should be listed as follows: Spyridoula Karveli, Petros Galanis, EiriniMarina Mitropoulou, Evangelos Karademas, & Christos Markopoulos. Likewise, the citation should be as follows: Karveli, S., Galanis, P., Mitropoulou, E. M., Karademas, E., & Markopoulos, C. (2023). The role of attachment styles on quality of life and distress among early-stage female breast cancer patients: A systematic review. Journal of Clinical Psychology in Medical Settings. https:// doi. org/ 10. 1007/ s10880- 023- 09940-w. © 2023 The Author(s)
One-shot learning for k-SAT
No full textConsider a k-SAT formula Φ where every variable appears at most d times, and let σ be a satisfying assignment of Φ sampled proportionally to e βm(σ) where m(σ) is the number of variables set to true and β is a real parameter. Given Φ and σ, can we learn the value of β efficiently?
This problem falls into a recent line of works about single-sample (“one-shot”) learning of Markov random fields. The k-SAT setting we consider here was recently studied by Galanis, Kandiros, and Kalavasis (SODA’24) where they showed that single-sample learning is possible when roughly d ≤ 2k/6.45 and impossible when d ≥ (k+1)2k−1 . Crucially, for their impossibility results they used the existence of unsatisfiable instances which, aside from the gap in d, left open the question of whether the feasibility threshold for one-shot learning is dictated by the satisfiability threshold of k-SAT formulas of bounded degree.
Our main contribution is to answer this question negatively. We show that one-shot learning for k-SAT is infeasible well below the satisfiability threshold; in fact, we obtain impossibility results for degrees d as low as k2 when β is sufficiently large, and bootstrap this to small values of β when dscales exponentially with k, via a probabilistic construction. On the positive side, we simplify the analysis of the learning algorithm and obtain significantly stronger bounds on d in terms of β. In particular, for the uniform case β → 0 that has been studied extensively in the sampling literature, our analysis shows that learning is possible under the condition d ≲ 2k/2. This is nearly optimal (up to constant factors) in the sense that it is known that sampling a uniformly-distributed satisfying assignment is NP-hard for d ≳ 2k/2
Unawareness of theorems
No full textThis 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 (J Econ Theory 144:977–993, 2009), Heifetz et al. (J Econ Theory 130:78–94, 25 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 (Ann Stat 4:1236–1239, 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
Financial complexity and trade
No full textWhat are the implications on trading activity if investors are not sophisticated enough to understand and evaluate trades that have a complex payoff structure? Can frictions generated by this type of financial complexity be so severe that they lead to a complete market freeze, like that of the recent financial crisis? We show that for smooth convex preferences, including subjective expected utility, even extreme complexity cannot halt trade, unlike what happens for non-smooth preferences, such as maxmin expected utility. In the latter case, policies that make complex securities easier to understand or investors more sophisticated have a positive welfare effect, as they allow for existing gains from trade to materialise
Theorems and unawareness
No full textThis paper provides a set-theoretic model of knowledge and unawareness, in which reasoning through theorems is employed. 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, Meier, and Schipper (2006) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event
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