Publications

Working Papers / R&Rs

Works In Progress

Average Loss Minimizing Choices, 2018, with Leonardo Pejsachowicz and Michael Richter

Abstract

Unawareness, Communication, and Incomplete Contracts: An Experiment, 2016,

with Felipe A. Araujo

Abstract

**Introspective Unawareness and Observable Choice. ** This paper considers a framework in which the decision makers's (DM) knowledge and awareness are explicitly modeled, as is her ability to reason about her own (un)awareness. The DM has a ranking over consumption alternatives that is informed by her epistemic
state (i.e., what she knows and what she is aware of), which can serve as a foundation for well known models.
The main result is a characterization, via observable choice, of introspective unawareness --a DM who is both
unaware of some information and aware she is unaware. In static environments, or when the DM is blind to
her own ignorance, the presence of unawareness does not produce any observable choice patterns. However,
under dynamic introspective unawareness, the DM will be unwilling to commit to making future choices,
even when given the
exibility to write a contingent plan that executes a choice conditional on the realization
of uncertain events. This is a behavior that cannot be explained by uncertainty alone (i.e., without appealing
to unawareness).

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**Learning the Krepsian State: Exploration Through Consumption. ** We take the Krepsian approach to provide a behavioral foundation for a class of responsive
subjective learning processes. In contrast to the standard subjective state space models, the resolution of
uncertainty regarding the true state is an endogenous process that depends on the decision maker's actions.
In addition, there need not be full resolution of uncertainty between periods. When the decision maker
chooses what to consume, she also chooses the information structure to which she will be exposed. When
she consumes outcomes, she learns her relative preference between them; after each consumption history,
the decision maker's information structure is a refinement of the previous information structure. We provide
the behavioral restrictions corresponding to an infinite horizon, recursive representation that exhibits such
a learning process. Moreover, through the incorporation of dynamics we are able to identify the set of
preferences the decision maker believes possible after each history of consumption. That is, we identify the
unique subjective state space without appealing to an environment with risk.

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**Exploration and Correlation.** We study the extent to which contemporaneous correlations across actions affect an agent’s preferences over the different strategies in exploration problems. We show that such correlations carry no economic content and do not affect the agent’s preferences and, in particular, her optimal strategy. We argue that for similar reasons there is an inherent partial identification of the beliefs in exploration problems. Nevertheless, even under the partial identification, we show there are explicit conditions allowing the modeler to test whether the agent is acting according to some Bayesian model.

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**Context Dependent Beliefs.** This paper examines a model where the set of available outcomes from which a decision maker must choose alters his perception of uncertainty. Specifically, this paper proposes a set of axioms such that each menu induces a subjective belief over an objective state-space. The decision maker’s preferences are dependent on the realization of the state. The resulting representation is analogous to state-dependent expected utility within each menu; the beliefs are menu-dependent and the utility index is not. Under the interpretation that a menu acts as an informative signal regarding the true state, the paper examines the behavioral restrictions that coincide with different signal structures: elemental (where each element of a menu is a conditionally independent signal) and partitional (where the induced beliefs form a partition of the state space).

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**Reference Dependence and Attitudes towards Uncertainty.** This paper characterizes a model of reference-dependence, where a state-contingent
contract (act) is evaluated by its expected value and its expected gain-loss utility. The expected utility of
an act serves as the reference point, hence gains (resp., losses) occur in states where the act provides an
outcome that is better (worse) than expected. Beliefs, preferences over outcomes, and a degree of reference-
dependence characterize the utility representation, and all are uniquely identified from behavior. Moreover,
we establish a link between reference-dependence and attitudes towards uncertainty. In particular, we show within our framework, loss aversion and reference dependence are equivalent to max-min expected utility.
Finally, we apply our model to sealed bid auctions where equilibrium bidding strategies are higher bids than
risk-neutrality, and hence are more closely aligned with experimental findings.

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**Rationalization and Robustness in Dynamic Games with Incomplete Information.** In this paper we show a formal connection between the epistemic characterization of a
solution concept and its robustness to the misspecification of parameters. This provides both an important
conceptual link and a direct method for checking robustness when the epistemic characterization is known.
We use this result to show extensive from rationality (EFR) is upper hemicontinuous. We also present a new framework that relaxes the common
knowledge restrictions regarding the space of payoff parameters. Then, we propose a new type of robustness,
s-robustness, to modeling errors of the player understanding of the space of uncertainty, which is of particular
importance in dynamic environments. We characterize this notion through our epistemic framework. Finally,
we provide a structure theorem for EFR with personal spaces of uncertainty that shows that no common
knowledge assumptions regarding the existence of dominance states are required to achieve generic dominance
solvability.

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**Distributional Uncertainty and Persuasion.** This paper investigates a Sender who tries to repeatedly persuade a Receiver. The Sender designs a signal structure, where signals regard a state that is drawn according to a distribution which is unknown to the Receiver. When information is disclosed more than once, each signal, in addition to its persuasive effect a la Kamenica and Gentzkow (2011), also changes the Receiver’s belief about the underlying distribution. The Sender’s optimal signal must balance these two effects. I characterize when the Receiver will learn the true distribution, and when the Sender prefers to keep the Receiver uncertain. Under mild conditions, the Sender’s private information is never fully revealed in equilibrium. I also consider a variant of the above model where the Sender has must publicly commit before becoming informed. I show a tight connection between the equilibria with and without public commitment: when commitment is flexible, the same set of optimization constraints dictate the optimal strategy in both environments. Capitalizing on this connection, I show that public commitment mechanisms need to be rigid in order to ensure that the true distribution over the state space will be revealed in equilibrium.

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** Disentangling Strict and Weak Choice in Random Expected Utility Models ** (joint with Roee Teper). We put forth a model of random choice in which precise choice frequencies of objects are identified only up to the frequency they are chosen by strict maxi- mization. The resulting primitive is a sub-additive capacity (i.e., set function). We provide simple restrictions on this primitive that are both necessary and sufficient for consistency with a random expected utility function. Thus, our model embeds both deterministic choice, regular random expected utility a la Gul and Pesendorfer (2006), and any combination between. We discuss several economic environments where such a primitive could be observed.

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** Unawareness, Communication, and Incomplete Contracts: An Experiment. ** (joint with Felipe A. Araujo). We develop an extension of the above model to strategic contracting environments and experiment test the predictions. There are two players: a broker is tasked with constructing a portfolio to (potentially) be sold to an investor. The set of events upon which these instruments may be contingent on is large, and may not be fully understood by either party. In our experiment, these events are all possible (English) words that can be formed using a set of six letters. For each word, the broker can construct a contract, whose payoff depends in part on the word. Payment is such that finding more words increases the expected value of the portfolio. The investor then values the portfolio of contracts after observing an informative signal about the set contracts. Our treatment is variation in the information asymmetry between the broker and investor and in the information disclosure policy of the broker. For the information variation, the investor is either shown the full set of possible words (fully aware) or is shown only the letters themselves (partially aware). For the disclosure variation, the signal shown to investors is either chosen randomly or by the broker. In addition to undervaluing the contracts as outlined by the above model, we predict that broker's will strategically withhold information that might increase the unawareness aversion of the investors. Thus, strategic incentives motivate agents to suppress information. We designed a browser based interface using the Python web-framework Django and SQL. We ran a pilot study in April of 2016, which indicated that subjects understood the interface and displayed some level of unawareness aversion, although the sample was too small for meaningful statistical analysis. We are currently applying for grants to fund a full trial.

** A Logic for Partial Awareness.** (joint with Joe Halpern). We develop a modal logic to capture partial awareness. The logic has three building blocks: objects, properties, and con- cepts. Properties are unary predicates on objects; concepts are Boolean combinations of properties. An agent can then be partially aware of a concept if she is aware of the concept in the abstract without being aware of the properties that de- fine it. The logic also allows for quantification over objects and properties so that the agent can reason about her own un- awareness. We then apply the logic to contracts. Contracts are syntactic objects that dictate outcomes based on the truth of formulae. The set of feasible contracts is limited by the for- mulae the agents are aware of. We show that when agents are unaware, referencing concepts that agents are only partially aware of can improve welfare.

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** Average Loss Minimizing Choices. ** (joint with Leonardo Pejsachowicz and Michael Richter). This paper consider a very simple behavioral model of reference dependence and loss aversion. A decision maker faces a decision problem, a set of objects from which he must choose. Each object can be decreibed by a vector of attributes. The DM takes as a refernce point the average over the decision problem. He chooses the object that minimizes the loss, evaluated according to a convex loss function. We provide a simple testible axiomatization of this choice behavior, and show that the loss function is identified from observables. This is generally not possible with more complex endogenous reference dependent behavior. The model imposes new behavioral predictions which we (plan to) take to the lab.

** Image Conscious Preferences ** An image conscious decision maker (DM) who cares not only about the physical consequences of his actions, but also how his actions are perceived by others. When a DM takes a choice, the resulting image is the set of preferences that are consistent with the observed choice. This paper axiomatizes the behavior of a DM who derives utility directly via consumption and also via the induced image. Because the image depends on what could have been chosen, the DM will display menu-dependent preferences. I consider two models: in the first, the modeler observes two stages of choice—over menus and then from the chosen menu; in the second, only the latter choices are observed. The two models share the same representation but uniqueness is obtained only in the first.

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