In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

In this paper, we consider the classic fair division problem of allocating m divisible items to n agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of n and m. In particular, we show a tight approximation bound of Θ(√n) for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of O(m^(2/3)) for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected value. We seek to achieve fairness among the options by revealing additional information to the decision maker and hence influencing its subsequent selection. To measure fairness, we adopt the notion of majorization, aiming at simultaneously approximately maximizing all symmetric, monotone, concave functions over the utilities of the options. As our main result, we design a novel information revelation policy that achieves a logarithmic-approximation to majorization in polynomial time. On the other hand, no policy, regardless of its running time, can achieve a constant-approximation to majorization. Our work is the first non-trivial majorization result in the Bayesian persuasion literature with multidimensional information sets.

Solving optimization problems leads to elegant and practical solutions in a wide variety of real-world applications. In many of those real-world applications, some of the information required to specify the relevant optimization problem is noisy, uncertain, and expensive to obtain. In this work, we study how much of that information needs to be queried in order to obtain an approximately optimal solution to the relevant problem. In particular, we focus on the shortest path problem in graphs with dynamic edge costs. We adopt the {\em first passage percolation} model from probability theory wherein a graph $G’$ is derived from a weighted base graph $G$ by multiplying each edge weight by an independently chosen, random number in $[1, \rho]$. Mathematicians have studied this model extensively when $G$ is a $d$-dimensional grid graph, but the behavior of shortest paths in this model is still poorly understood in general graphs. We make progress in this direction for a class of graphs that resemble real-world road networks. Specifically, we prove that if $G$ has a constant continuous doubling dimension, then for a given $s-t$ pair, we only need to probe the weights on $((\rho \log n )/ \epsilon)^{O(1)}$ edges in $G’$ in order to obtain a $(1 + \epsilon)$-approximation to the $s-t$ distance in $G’$. We also generalize the result to a correlated setting and demonstrate experimentally that probing improves accuracy in estimating $s-t$ distances.

A seller is pricing identical copies of a good to a stream of unit-demand buyers. Each buyer has a value on the good as his private information. The seller only knows the empirical value distribution of the buyer population and chooses the revenue-optimal price. We consider a widely studied third-degree price discrimination model where an information intermediary with perfect knowledge of the arriving buyer's value sends a signal to the seller, hence changing the seller's posterior and inducing the seller to set a personalized posted price. Prior work of Bergemann, Brooks, and Morris (American Economic Review, 2015) has shown the existence of a signaling scheme that preserves seller revenue, while always selling the item, hence maximizing consumer surplus. In a departure from prior work, we ask whether the consumer surplus generated is fairly distributed among buyers with different values. To this end, we aim to maximize functions of buyers’ welfare that reward more balanced surplus allocations.

We consider the classical multiwinner election problem where the goal is to choose a subset of k unit-sized candidates (called committee) given utility functions of the voters. We allow arbitrary additional constraints on the chosen committee, and the utilities of voters to belong to a very general class of set functions called β-self bounding. When β = 1, this class includes XOS (and hence, submodular and additive) utilities as special cases. We define a novel generalization of core stability called restrained core to handle constraints on the committee, and consider multiplicative approximations on the utility under this notion.

Motivated by civic problems such as participatory budgeting and multiwinner elections, we consider the problem of public good allocation: Given a set of indivisible projects (or candidates) of different sizes, and voters with different monotone utility functions over subsets of these candidates, the goal is to choose a budget-constrained subset of these candidates (or a committee) that provides fair utility to the voters. The notion of fairness we adopt is that of core stability from cooperative game theory: No subset of voters should be able to choose another blocking committee of proportionally smaller size that provides strictly larger utility to all voters that deviate. The core provides a strong notion of fairness, subsuming other notions that have been widely studied in computational social choice. It is well-known that an exact core need not exist even when utility functions of the voters are additive across candidates. We therefore relax the problem to allow approximation: Voters can only deviate to the blocking committee if after they choose any extra candidate (called an additament), their utility still increases by an α factor. If no blocking committee exists under this definition, we call this an α-core. Our main result is that an α-core, for α < 67.37, always exists when utilities of the voters are arbitrary monotone submodular functions, and this can be computed in polynomial time. This result improves to α < 9.27 for additive utilities, albeit without the polynomial time guarantee. Our results are a significant improvement over prior work that only shows logarithmic approximations for the case of additive utilities. We complement our results with a lower bound of α > 1.015 for submodular utilities, and a lower bound of any function in the number of voters and candidates for general monotone utilities.

This paper introduces the targeted sampling model in optimal auction design. In this model, the seller may specify a quantile interval and sample from a buyer's prior restricted to the interval. This can be interpreted as allowing the seller to, for example, examine the top 40% bids from previous buyers with the same characteristics. The targeting power is quantified with a parameter Δ ∈ [0, 1] which lower bounds how small the quantile intervals could be. When Δ = 1, it degenerates to Cole and Roughgarden's model of i.i.d. samples; when it is the idealized case of Δ = 0, it degenerates to the model studied by [7]. For instance, for n buyers with bounded values in [0, 1], ~O(ε-1) targeted samples suffice while it is known that at least ~Ømega(n ε-2) i.i.d. samples are needed. In other words, targeted sampling with sufficient targeting power allows us to remove the linear dependence in n, and to improve the quadratic dependence in ε-1 to linear. In this work, we introduce new technical ingredients and show that the number of targeted samples sufficient for learning an ε-optimal auction is substantially smaller than the sample complexity of i.i.d. samples for the full spectrum of Δ ∈ [0, 1). Even with only mild targeting power, i.e., whenever Δ = o(1), our targeted sample complexity upper bounds are strictly smaller than the optimal sample complexity of i.i.d. samples.

We consider the problem of purchasing data for machine learning or statistical estimation. The data analyst has a budget to purchase datasets from multiple data providers. She does not have any test data that can be used to evaluate the collected data and can assign payments to data providers solely based on the collected datasets. We consider the problem in the standard Bayesian paradigm and in two settings: (1) data are only collected once; (2) data are collected repeatedly and each day's data are drawn independently from the same distribution. For both settings, our mechanisms guarantee that truthfully reporting one's dataset is always an equilibrium by adopting techniques from peer prediction: pay each provider the mutual information between his reported data and other providers' reported data. Depending on the data distribution, the mechanisms can also discourage misreports that would lead to inaccurate predictions. Our mechanisms also guarantee individual rationality and budget feasibility for certain underlying distributions in the first setting and for all distributions in the second setting.