24 research outputs found
Efficiently Characterizing Games Consistent with Perturbed Equilibrium Observations
In this thesis, we study the problem of characterizing the set of games that are consistent with observed equilibrium play, a fundamental problem in econometrics. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem, for many classes of games and observation models of interest. Our approach provides a sharp, computationally efficient characterization of the extent to which a particular set of observations constrains the space of games that could have generated them. This allows us to solve a number of variants of this problem as well as to quantify the power of games from particular classes (e.g., zero-sum, potential, linearly parameterized) to explain player behavior.
We illustrate our approach with numerical simulations.</p
Access to Population-Level Signaling as a Source of Inequality
We identify and explore differential access to population-level signaling
(also known as information design) as a source of unequal access to
opportunity. A population-level signaler has potentially noisy observations of
a binary type for each member of a population and, based on this, produces a
signal about each member. A decision-maker infers types from signals and
accepts those individuals whose type is high in expectation. We assume the
signaler of the disadvantaged population reveals her observations to the
decision-maker, whereas the signaler of the advantaged population forms signals
strategically. We study the expected utility of the populations as measured by
the fraction of accepted members, as well as the false positive rates (FPR) and
false negative rates (FNR).
We first show the intuitive results that for a fixed environment, the
advantaged population has higher expected utility, higher FPR, and lower FNR,
than the disadvantaged one (despite having identical population quality), and
that more accurate observations improve the expected utility of the advantaged
population while harming that of the disadvantaged one. We next explore the
introduction of a publicly-observable signal, such as a test score, as a
potential intervention. Our main finding is that this natural intervention,
intended to reduce the inequality between the populations' utilities, may
actually exacerbate it in settings where observations and test scores are
noisy
Data: Implications for Markets and for Society
Every day, massive amounts of data are gathered, exchanged, and used to run statistical computations, train machine learning algorithms, and inform decisions on individuals and populations. The quick rise of data, the need to exchange and process it, to take data privacy concerns into account, and to understand how it affects decision-making, introduce many new and interesting economic, game theoretic, and algorithmic challenges.
The goal of this thesis is to provide theoretical foundations to approach these challenges. The first part of this thesis focuses on the design of mechanisms that purchase then aggregate data from many sources, in order to perform statistical tasks. The second part of this thesis revolves around the societal concerns associated with the use of individuals' data. The first such concern we examine is that of privacy, when using sensitive data about individuals in statistical computations; we focus our attention on how privacy constraints interact with the task of designing mechanisms for acquisition and aggregation of sensitive data. The second concern we focus on is that of fairness in decision-making: we aim to provide tools to society that help prevent discrimination against individuals and populations based on sensitive attributes in their data, when making important decisions about them. Finally, we end this thesis on a study of the interactions between data and strategic behavior. There, we see data as a source of information that informs and affects agents' incentives; we study how information revelation impacts agent behavior in auctions, and in turn how a seller should design auctions that take such information revelation into account.</p
Optimal Data Acquisition for Statistical Estimation
We consider a data analyst's problem of purchasing data from strategic agents
to compute an unbiased estimate of a statistic of interest. Agents incur
private costs to reveal their data and the costs can be arbitrarily correlated
with their data. Once revealed, data are verifiable. This paper focuses on
linear unbiased estimators. We design an individually rational and incentive
compatible mechanism that optimizes the worst-case mean-squared error of the
estimation, where the worst-case is over the unknown correlation between costs
and data, subject to a budget constraint in expectation. We characterize the
form of the optimal mechanism in closed-form. We further extend our results to
acquiring data for estimating a parameter in regression analysis, where private
costs can correlate with the values of the dependent variable but not with the
values of the independent variables
Downstream Effects of Affirmative Action
We study a two-stage model, in which students are 1) admitted to college on
the basis of an entrance exam which is a noisy signal about their
qualifications (type), and then 2) those students who were admitted to college
can be hired by an employer as a function of their college grades, which are an
independently drawn noisy signal of their type. Students are drawn from one of
two populations, which might have different type distributions. We assume that
the employer at the end of the pipeline is rational, in the sense that it
computes a posterior distribution on student type conditional on all
information that it has available (college admissions, grades, and group
membership), and makes a decision based on posterior expectation. We then study
what kinds of fairness goals can be achieved by the college by setting its
admissions rule and grading policy. For example, the college might have the
goal of guaranteeing equal opportunity across populations: that the probability
of passing through the pipeline and being hired by the employer should be
independent of group membership, conditioned on type. Alternately, the college
might have the goal of incentivizing the employer to have a group blind hiring
rule. We show that both goals can be achieved when the college does not report
grades. On the other hand, we show that under reasonable conditions, these
goals are impossible to achieve even in isolation when the college uses an
(even minimally) informative grading policy
Access to Population-Level Signaling as a Source of Inequality
We identify and explore differential access to population-level signaling (also known as information design) as a source of unequal access to opportunity. A population-level signaler has potentially noisy observations of a binary type for each member of a population and, based on this, produces a signal about each member. A decision-maker infers types from signals and accepts those individuals whose type is high in expectation. We assume the signaler of the disadvantaged population reveals her observations to the decision-maker, whereas the signaler of the advantaged population forms signals strategically. We study the expected utility of the populations as measured by the fraction of accepted members, as well as the false positive rates (FPR) and false negative rates (FNR).
We first show the intuitive results that for a fixed environment, the advantaged population has higher expected utility, higher FPR, and lower FNR, than the disadvantaged one (despite having identical population quality), and that more accurate observations improve the expected utility of the advantaged population while harming that of the disadvantaged one. We next explore the introduction of a publicly-observable signal, such as a test score, as a potential intervention. Our main finding is that this natural intervention, intended to reduce the inequality between the populations' utilities, may actually exacerbate it in settings where observations and test scores are noisy
Non-Exploitable Protocols for Repeated Cake Cutting
We introduce the notion of exploitability in cut-and-choose protocols for repeated cake cutting. If a cut-and-choose protocol is repeated, the cutter can possibly gain information about the chooser from her previous actions, and exploit this information for her own gain, at the expense of the chooser. We define a generalization of cut-and-choose protocols - forced-cut protocols - in which some cuts are made exogenously while others are made by the cutter, and show that there exist non-exploitable forced-cut protocols that use a small number of cuts per day: When the cake has at least as many dimensions as days, we show a protocol that uses a single cut per day. When the cake is 1-dimensional, we show an adaptive non-exploitable protocol that uses 3 cuts per day, and a non-adaptive protocol that uses n cuts per day (where n is the number of days). In contrast, we show that no non-adaptive non-exploitable forced-cut protocol can use a constant number of cuts per day. Finally, we show that if the cake is at least 2-dimensional, there is a non-adaptive non-exploitable protocol that uses 3 cuts per day