## Working Papers

# Dynamic Choice of Information Sources

## October 1, 2020

An agent has to choose among a finite set of actions with payoffs depending on an unknown state of the world with two (possibly correlated) binary components, (θ1, θ2), θi∈{0,1}. Before making the choice, the agent can learn about the state by dynamically allocating his limited attention over two information sources, modelled as search processes for conclusive evidence of θ1=1 or θ2=1. In the special case where θ1+θ2 ≤1, the agent searches for the most probable evidence up to some time t*, and after that he continues by challenging his current beliefs in the most effective way. The agent never changes his allocation of attention after t*. When the state (1,1) is possible, the attention rule before t* is different. Sufficient conditions for t*>0 are given. A negative correlation between the state components increases t*.

# Imposing Commitment to Rein in Overconfidence in Learning (joint with Marcelo A. Fernandez and Arina Nikandrova)

## December 13, 2021

A rational principal delegates learning to an overconfident agent who overestimates the precision of the information he collects. The principal chooses between two contracts: commitment and flexible. Under the former, the agent commits to the duration of learning in advance; under the latter, the agent decides when to stop learning in real time. The principal would never choose to tie the hands of a rational agent by forcing him to commit. In contrast, when the agent is sufficiently overconfident, the principal optimally offers the commitment contract. When the principal can choose both the contract and the agent's level of overconfidence, selecting the rational agent is suboptimal when the cost of learning is sufficiently high.

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

## February 2, 2020

Two agents sincerely exchange their best guesses about the state of the world infinitely many times. When each agent places a small positive probability on the event that her opponent is of some finite level of reasoning and initial disagreement is large enough (that is, private signals are strong and different), permanent and large disagreement is possible even for infinitely sophisticated agents.

# Privacy Paradox: When Hiding in Plain Sight Works (joint with Arina Nikandrova)

## August 3, 2021

A hider publicly commits to the number of seekers and then privately gets involved in a story, which may be compromising. Each seeker aims to be the first to learn and report a compromising story. The seekers learn the story privately and in continuous time. With more seekers, the hider's story gets revealed at a faster rate, but each seeker gets discouraged and ceases learning more quickly. To reduce the probability of a compromising report, the hider may optimally choose infinitely many seekers. Nevertheless, the hider unambiguously benefits from making it harder for each seeker to learn her story.

## Work in Progress

# Diversity and Communication (joint with Miaomiao Dong)

We study optimal diversity in a team of two agents where the decision is delegated to a single agent. As a function of the cost of communication between the agents, the optimal diversity has a hump-shaped form, balancing two forces: higher diversity increases the combined knowledge of the team but hinders communication. When the cost of communication is low, the first force prevails, and reducing the cost increases the optimal diversity. When the cost of communication is high, the second force prevails, and reducing the cost decreases the optimal diversity.

# Experimentation on a Content Aggregator (joint with Claudia Herresthal and Arina Nikandrova)

## Archive

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

## Sept 27, 2017

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.

# Stochastic Choice in Criterion Space

## May 30, 2014

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.