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.

Admissibility and Event-Rationality

We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other players' strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that common belief of event-rationality (RCBER) implies that players play strategies in S1W, that is, admissible strategies that also survive iterated elimination of dominated strategies (Dekel and Fudenberg (1990)). We strengthen standard belief to validated belief and we show that event-rationality and common validated belief of event-rationality (RCvBER) implies that players play iterated admissible strategies (IA). We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, and hence we obtain epistemic criteria for SinfW and IA.

Admissibility and event-rationality

Brandenburger et al. (2008) establish epistemic foundations for rationality and common assumption of rationality (RCAR), where rationality includes admissibility, using lexicographic type structures. Their negative result that RCAR is empty whenever the type structure is complete and continuous suggests that iterated admissibility (IA) requires players to have prior knowledge about each other, and therefore is a strong solution concept, not at the same level as iterated elimination of strongly dominated strategies (IEDS). We follow an alternative approach using standard type structures and show that IA can be generated in a complete and continuous type structure. A strategy is event-rational if it is a best response to a conjecture, as usual, and in addition it passes a “tie-breaking†test based on a set E of strategies of the other player. Event-rationality and common belief in event-rationality (RCBER) is characterized by a solution concept we call hypo-admissible sets and, in a complete structure, generates the strategies that are admissible and survive the iterated elimination of strongly dominated strategies (Dekel and Fudenberg (1990)). Extending event-rationality by adding what a player is certain about the other’s strategies as a tie-breaking set to each round of mutual belief we get common belief of extended event-rationality (RCBeER), which generates a more restrictive solution concept than the SAS (Brandenburger et al. (2008)) and in a complete structure produces the IA strategies. Contrary to the negative result in Brandenburger et al. (2008), we show that RCBER and RCBeER are nonempty in complete, continuous and compact type structures, therefore providing an epistemic criterion for IA <br><br> Keywords; epistemic game theory, admissibility, iterated weak dominance, common knowledge, rationality, completeness

Design Spaces in Visual Analytics Based on Goals: Analytical Behaviour, Exploratory Investigation, Information Design & Perceptual Tasks

This paper considers a number of perspectives on design spaces in visual analytics and proposes a new set of four design spaces, based on user goals. Three of the user goals are derived from the literature and are categorised under the terms exploratory investigation, perceptual tasks, and information design. The fourth goal is categorised as analytical behaviour; a recently defined term referring to the study of decision-making facilitated by visual analytics. This paper contributes to the literature on decision-making in visual analytics with a survey of real-world applications within the analytical behaviour design space and by providing a new perspective on design spaces. Central to our analysis is the introduction of decision concepts and theories from economics into a visual analytics context. Given the recent interest in decision-making we wanted to understand the emerging topic of analytical behaviour as a design space and found it necessary to look at more than just decision-making to make a valuable contribution. The result is an initial framework suitable for use in the analysis or design of analytical behaviour applications

Heterogeneity and clustering of defaults

This paper studies how the degree of heterogeneity among hedge funds' demand orders for a risky asset affects the possibility of their defaults being clustered. We find that fire-sales caused by margin calls is a necessary, yet not a sufficient condition for defaults to be clustered. We show that when the degree of heterogeneity is sufficiently high, poorly performing HFs are able to obtain a higher than usual market share, which leads to an improvement of their performance. Consequently, their survival time is prolonged, increasing the probability of them remaining in operation until the downturn of the next leverage cycle. This leads to an increase in the probability of poorly and high-performing hedge funds to default in sync at a later time, and thus also in the probability of collective defaults. Our analytical results establish a connection between the nontrivial aggregate statistics and the presence of infinite memory in the process governing the hedge funds' defaults

Trade and the value of information under unawareness

The 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

Concern for relative standing and deception

We report results from a sender-receiver cheap talk game, which explores whether an individual's decision to deceive is influenced by a concern for relative standing in a reference group. We show theoretically that positively biased senders, who think they are higher in the deception distribution than they actually are, will correct their beliefs and increase their cheating, when presented with information on the actual deception distribution. Hence, a predominantly positively biased group of senders will increase its average deception. Moreover, within a group, being more positively biased implies cheating less. The experimental data confirm both of these hypothese

Six easy models of international trade theory

This book provides a short and concise introduction to the main theories of international trade, addressing the following questions. Are there gains for a country that engages in free trade? Which goods does it export and import? What happens to its income distribution? What are the implications for consumers and producers when it restricts trade, for example by imposing import tariffs

Speculation under unawareness

“No trade” theorems establish that, in various trading environments, investors who share a common prior will not engage in speculation, as long as expected utility, Bayesian updating and full awareness are imposed. We relax the last assumption by allowing for asymmetric unawareness and examine under which conditions speculative behaviour emerges. We find that if common knowledge is assumed (as in the settings of Aumann, 1976 and Milgrom and Stokey, 1982), unawareness cannot generate speculation. This is not true, however, in settings where no common knowledge is assumed, such as speculation in equilibrium (Geanakoplos, 1989) and betting that is always beneficial (Morris, 1994), unless stronger conditions on awareness are imposed

Syntactic foundations for unawareness of theorems

We 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