arXiv subjects

Krishna Dasaratha

Publications and source records attributed to Krishna Dasaratha.

18 recordsLinked to original sources

arXiv2026

Attention and Social Learning

In an incentivized laboratory experiment, we study how people account for and respond to others' incentives for paying attention. Participants learn a binary state from an attention task under high or low accuracy incentives. We ask subjects to predict their peers' accuracy based on the peers' incentives and to aggregate answers from multiple peers with different incentives. Most subjects fail to consistently understand that peers with stronger incentives are more accurate, and these subjects also perform worse in individual attention tasks. Subjects also participate in a social-learning task where they first learn the binary state from an attention task, then observe a peer's guess about the state in the same task, and finally make a guess themselves. We find behavior in these tasks is inconsistent with leading models of flexible costly information acquisition. In particular, subjects fail to pay more attention when paired with lower incentive peers. Overall, we find that many decision-makers do not respond to others' incentives for accuracy even when those incentives are transparent.

econ.TH↗

arXiv2026

Network Interventions: Targeting Agents or Targeting Links?

Consider a network game with linear best responses and spillovers between players, and let agents endogenously choose their links. A planner considers interventions to subsidize actions and/or links between players, aiming to maximize a welfare objective. The structure of an optimal intervention is shaped by the intrinsic value that links provide to agents. When this value is non-negative, it is optimal to focus only on subsidizing actions. When it is negative, we give conditions under which it is necessary to include link subsidies. This reverses the basic structure of the optimal intervention in settings with exogenous links.

econ.TH↗

arXiv2025

Markets for Models

Motivated by the prevalence of prediction problems in the economy, we study markets in which firms sell models to a consumer to help improve their prediction. Firms decide whether to enter, choose models to train on their data, and set prices. The consumer can purchase multiple models and use a weighted average of the models bought. Market outcomes can be expressed in terms of the \emph{bias-variance decompositions} of the models that firms sell. We give conditions when symmetric firms will choose different modeling techniques, e.g., each using only a subset of available covariates. We also show firms can choose inefficiently biased models or inefficiently costly models to deter entry by competitors.

econ.TH↗

arXiv2024

Incentive Design with Spillovers

A principal uses payments conditioned on stochastic outcomes of a team project to elicit costly effort from the team members. We develop a multi-agent generalization of a classic first-order approach to contract optimization by leveraging methods from network games. The main results characterize the optimal allocation of incentive pay across agents and outcomes. Incentive optimality requires equalizing, across agents, a product of (i) individual productivity (ii) organizational centrality and (iii) responsiveness to monetary incentives. We specialize the model to explore several applied questions, including whether compensation should reward individual ability or collaborativeness and how the strength of complementarities shapes pay dispersion.

econ.TH↗

arXiv2024

Optimal Bailouts in Diversified Financial Networks

Widespread default involves substantial deadweight costs which could be countered by injecting capital into failing firms. Injections have positive spillovers that can trigger a repayment cascade. But which firms should a regulator bailout so as to minimize the total injection of capital while ensuring solvency of all firms? While the problem is, in general, NP-hard, for a wide range of networks that arise from a stochastic block model, we show that the optimal bailout can be implemented by a simple policy that targets firms based on their characteristics and position in the network. Specific examples of the setting include core-periphery networks.

econ.TH↗

arXiv2023

Virus Dynamics with Behavioral Responses

Motivated by epidemics such as COVID-19, we study the spread of a contagious disease when behavior responds to the disease's prevalence. We extend the SIR epidemiological model to include endogenous meeting rates. Individuals benefit from economic activity, but activity involves interactions with potentially infected individuals. The main focus is a theoretical analysis of contagion dynamics and behavioral responses to changes in risk. We obtain a simple condition for when public-health interventions or variants of a disease will have paradoxical effects on infection rates due to risk compensation. Behavioral responses are most likely to undermine public-health interventions near the peak of severe diseases.

q-bio.PE↗

arXiv2023

Equity Pay In Networked Teams

A group of agents each exert effort to produce a joint output, with the complementarities between their efforts represented by a (weighted) network. Under equity compensation, a principal motivates the agents to work by giving them shares of the output. We describe the optimal equity allocation. It is characterized by a neighborhood balance condition: any two agents receiving equity have the same (weighted) total equity assigned to their neighbors. We also study the problem of selecting the team of agents who receive positive equity, and show this team must form a tight-knit subset of the complementarity network, with any pair being complementary to one another or jointly to another team member. Finally, we give conditions under which the amount of equity used for compensation is increasing in the strength of a team's complementarities and discuss several other applications.

econ.TH↗

arXiv2022

Learning from Neighbors about a Changing State

Agents learn about a changing state using private signals and their neighbors' past estimates of the state. We present a model in which Bayesian agents in equilibrium use neighbors' estimates simply by taking weighted sums with time-invariant weights. The dynamics thus parallel those of the tractable DeGroot model of learning in networks, but arise as an equilibrium outcome rather than a behavioral assumption. We examine whether information aggregation is nearly optimal as neighborhoods grow large. A key condition for this is signal diversity: each individual's neighbors have private signals that not only contain independent information, but also have sufficiently different distributions. Without signal diversity $\unicode{x2013}$ e.g., if private signals are i.i.d. $\unicode{x2013}$ learning is suboptimal in all networks and highly inefficient in some. Turning to social influence, we find it is much more sensitive to one's signal quality than to one's number of neighbors, in contrast to standard models with exogenous updating rules.

econ.TH↗

arXiv2022

Learning from Viral Information

Motivated by social media, we study an equilibrium model of agents interacting with and learning from each other's signals. Rational agents arrive sequentially, observe a signal (corresponding to a news story) and a sample of predecessors' signals (corresponding to a news feed), and decide which of these signals to endorse. The observed sample is jointly determined by predecessors' endorsement behavior and a sampling rule (capturing a platform algorithm). We focus on how often the sampling rule selects more viral (i.e., widely endorsed) signals. Showing agents viral signals can increase information aggregation, but it can also generate steady states where most endorsed signals are wrong. These misleading steady states self-perpetuate, as agents who observe wrong signals develop wrong beliefs, and thus rationally continue to endorse them. We highlight several consequences of our results for social-media platforms.

econ.TH↗

arXiv2022

Innovation and Strategic Network Formation

We study a model of innovation with a large number of firms that create new technologies by combining several discrete ideas. These ideas are created via private investment and spread between firms. Firms face a choice between secrecy, which protects existing intellectual property, and openness, which facilitates learning from others. Their decisions determine interaction rates between firms, and these interaction rates enter our model as link probabilities in a learning network. Higher interaction rates impose both positive and negative externalities, as there is more learning but also more competition. We show that the equilibrium learning network is at a critical threshold between sparse and dense networks. At equilibrium, the positive externality from interaction dominates: the innovation rate and welfare would be dramatically higher if the network were denser. So there are large returns to increasing interaction rates above the critical threshold. Nevertheless, several natural types of interventions fail to move the equilibrium away from criticality. One effective policy solution is to introduce informational intermediaries, such as public innovators who do not have incentives to be secretive. These intermediaries can facilitate a high-innovation equilibrium by transmitting ideas from one private firm to another.

econ.TH↗

arXiv2021

An Experiment on Network Density and Sequential Learning

We conduct a sequential social-learning experiment where subjects each guess a hidden state based on private signals and the guesses of a subset of their predecessors. A network determines the observable predecessors, and we compare subjects' accuracy on sparse and dense networks. Accuracy gains from social learning are twice as large on sparse networks compared to dense networks. Models of naive inference where agents ignore correlation between observations predict this comparative static in network density, while the finding is difficult to reconcile with rational-learning models.

econ.TH↗

arXiv2019

Aggregative Efficiency of Bayesian Learning in Networks

When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are log-linear functions of observations and admit a signal-counting interpretation of accuracy. Networks where agents observe multiple neighbors but not their common predecessors confound information, and even a small amount of confounding can lead to much lower accuracy. In a class of networks where agents move in generations and observe the previous generations, we quantify the information loss with an aggregative efficiency index. Aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Later generations contribute little additional information, even when generations are arbitrarily large and agents observe arbitrarily far into the past.

econ.TH↗

arXiv2017

Distributions of Centrality on Networks

We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random network models to accommodate data limitations or prove asymptotic results. Our main theorems show that on large random networks, centrality measures are close to their expected values with high probability. We illustrate the economic consequences of these results by presenting three applications: (1) In network formation models based on community structure (called stochastic block models), we show network segregation and differences in community size produce inequality. Benefits from peer effects tend to accrue disproportionately to bigger and better-connected communities. (2) When link probabilities depend on geography, we can compute and compare the centralities of agents in different locations. (3) In models where connections depend on several independent characteristics, we give a formula that determines centralities 'characteristic-by-characteristic'. The basic techniques from these applications, which use the main theorems to reduce questions about random networks to deterministic calculations, extend to many network games.

cs.SI↗

arXiv2017

Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences

The Stern diatomic sequence is closely linked to continued fractions via the Gauss map on the unit interval, which in turn can be understood via systematic subdivisions of the unit interval. Higher dimensional analogues of continued fractions, called multidimensional continued fractions, can be produced through various subdivisions of a triangle. We define triangle partition-Stern sequences (TRIP-Stern sequences for short), higher-dimensional generalizations of the Stern diatomic sequence, from the method of subdividing a triangle via various triangle partition algorithms. We then explore several combinatorial results about TRIP-Stern sequences, which may be used to give rise to certain well-known sequences. We finish by generalizing TRIP-Stern sequences and presenting analogous results for these generalizations.

math.CO↗

arXiv2017

Network Structure and Naive Sequential Learning

We study a sequential-learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors' actions. They weigh these actions according the strengths of their social connections to different predecessors. We show this rule arises endogenously when agents wrongly believe others act solely on private information and thus neglect redundancies among observations. We provide a simple linear formula expressing agents' actions in terms of network paths and use this formula to characterize the set of networks where naive agents eventually learn correctly. This characterization implies that, on all networks where later agents observe more than one neighbor, there exist disproportionately influential early agents who can cause herding on incorrect actions. Going beyond existing social-learning results, we compute the probability of such mislearning exactly. This allows us to compare likelihoods of incorrect herding, and hence expected welfare losses, across network structures. The probability of mislearning increases when link densities are higher and when networks are more integrated. In partially segregated networks, divergent early signals can lead to persistent disagreement between groups.

econ.GN↗

arXiv2016

Rational points on twisted K3 surfaces and derived equivalences

Using a construction of Hassett--Várilly-Alvarado, we produce derived equivalent twisted K3 surfaces over $\mathbb{Q}$, $\mathbb{Q}_2$, and $\mathbb{R}$, where one has a rational point and the other does not. This answers negatively a question recently raised by Hassett and Tschinkel.

math.NT↗

arXiv2014

Cubic Irrationals and Periodicity via a Family of Multi-dimensional Continued Fraction Algorithms

We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a, a-a^2) is purely periodic with respect to an element in the family. These cubic irrationals seem to be quite natural, as we show that, for every cubic number field, there exists a pair (u,u') with u a unit in the cubic number field (or possibly the quadratic extension of the cubic number field by the square root of the discriminant) such that (u,u') has a periodic multidimensional continued fraction expansion under one of the maps in the family generated by the initial five maps. Thus these results are built on a careful technical analysis of certain units in cubic number fields and our family of multi-dimensional continued fractions. We then recast the linking of cubic irrationals with periodicity to the linking of cubic irrationals with the construction of a matrix with nonnegative integer entries for which at least one row is eventually periodic.

math.NT↗

arXiv2012

A Generalized Family of Multidimensional Continued Fractions: TRIP Maps

Most well-known multidimensional continued fractions, including the Mönkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a family of multidimensional continued fractions by permuting the vertices of these triangles before and after each subdivision. We obtain an even larger class of multidimensional continued fractions by composing the maps in the family. These include the algorithms of Brun, Parry-Daniels and Güting. We give criteria for when multidimensional continued fractions associate sequences to unique points, which allows us to determine when periodicity of the corresponding multidimensional continued fraction corresponds to pairs of real numbers being cubic irrationals in the same number field.

math.NT↗