## Working Papers

The state of the world has two (possibly correlated) binary components, (θ1,θ2), θi belongs to {0,1}. An agent can search for conclusive evidence of θi=1. The model is dynamic with endogenous stopping time. No matter what the actions are (the agent chooses from these actions when he stops the search) and no matter what the payoffs from these actions are in different states, any optimal strategy consists of two phases. In a special case when θ1+θ2<=1, the agent searches in the most promising direction during the first phase (possibly changing the direction as the search progresses) and completely ignores one of the state components during the second phase. Applying the result, I show (1) how the availability of sources for collecting information resolves disagreement between groups with opposed interests, and (2) what a policy maker can achieve when an expert is restricted to report the state.

# Dynamic Choice of Information Sources (job market paper)

## June 3, 2019

We present a dynamic model that illustrates three forces that shape the effect of overconfidence (overprecision of consumed information) on the amount of collected information. The first force comes from overestimating the precision of the next consumed piece of information. The second force is related to overestimating the precision of already collected information. The third force reflects the discrepancy between how much information the agent expects to collect and how much information he actually collects in expectation. The first force pushes an overconfident agent to collect more information, while the second and the third forces work in the other direction.

# Implications of Overconfidence on Information Investment (joint with Marcelo A. Fernandez)

## Oct 22, 2017

Two agents sincerely exchange their best guesses about the state of the world infinitely many times. We adapt the cognitive hierarchical (CH) model to the belief formation process. In contrast to the classical CH model, we do not require the belief distribution about the levels of thinking to be consistent with the realized distribution and assume everybody is of level infinity. When the agents place probability p close to 1 to the event that everybody is indeed of level infinity, we get almost common knowledge of rationality. For any p close to 1, we can always find the initial level of disagreement high enough so that the agents will never agree.

# Disagreement Under Almost Common Knowledge of Rationality (joint with Emiliano Catonini)

## July 1, 2019

## Work in Progress

The amount of information produced every day is staggering and Internet makes a lot of this information available almost for free. We argue that free access to information does not guarantee that it is going to be used for making decisions. More precisely, sufficient conditions for cheap payoff-relevant information not to be collected in a symmetric equilibrium are: (1) sufficiently many people have access to this information, and (2) the usefulness of information to a person highly depends on other people's actions. Primary examples are elections (when free-riding discourages information collection) and financial markets (when competition is too vigorous). Our conclusion alleviates concerns over making private information available in public domain: publicity might render information useless, thus effectively protecting sensitive information from prying eyes.

# When Should We Care About Privacy? Information Collection in Games (joint with Arina Nikandrova)

## Archive

Theoretical paper DeMarzo, Vayanos, and Zwiebel (2003) proposes a model of information aggregation in networks when individuals are subject to persuasion bias. The term "persuasion bias" refers to a particular form of boundedly rational behavior when individuals connected into a network do not account for repetition in the information they acquire. We argue that under the assumption that agents form their beliefs as a weighted average of all information available to them, the persuasion bias assumption is equivalent to a generalized version of the famous DeGroot model (DeGroot (1974)). We test the persuasion bias hypothesis against the (generalized) Bayesian updating model and find support for the persuasion bias hypothesis. We also found a positive correlation between how well a subject fits the generalized DeGroot model, compared to the alternative generalized Bayesian updating model, and their performance in the experiment. Data suggest that the generalized DeGroot model better accommodates other subjects' deviations from equilibrium, which explains the positive correlation.

# Are People Subject to Persuasion Bias? Test of DeGroot Model (joint with Li Song)

## Sept 27, 2017

Many experiments demonstrate that an individual's choice decisions are inconsistent. Following Luce (1959) and Block, Marschak, et al. (1960), a random choice approach to this problem has become very popular. It posits the existence of a probabilistic choice function that describes the probability of choosing an alternative from a given set of options. This paper contributes to the theoretical literature that narrows the class of random choice functions. Each alternative can be fully characterized by a vector in a n-dimensional space. A decision maker pays attention only to a randomly chosen subset of coordinates (or criteria) each time he faces a set of alternatives to choose from. Given this randomly chosen subset, he is perfectly rational, that is he chooses according to some strict preference ordering. For this procedure to be well-defined, the preference ordering must be separable with respect to criteria. In other words, the preference of the decision maker over any two alternatives should not depend on the characteristics that these alternatives have in common. This paper characterizes all systems of choice probabilities that are induced by this choice procedure.