arXiv subjects

Yakov Babichenko

Publications and source records attributed to Yakov Babichenko.

At least 19 recordsLinked to original sources

arXiv2026

Testing Decision Makers without Counterfactuals

A decision-maker (DM) repeatedly makes choices under uncertainty in a bandit environment, where only the realization of the chosen arm is observed. Another competing agent, the adviser (AD), repeatedly provides recommendations, but the realizations of these recommendations are unobserved unless they coincide with the DM's choice. Both agents possess partial information about the arms' realizations. The central question we focus on is whether, in the long run, an outside observer can identify which agent is more informed based solely on the observed decisions, recommendations, and arm realizations. A test selects one of the agents based on the observed data. We focus primarily on the class of scoring tests, which assign a numerical score to each observation and select the agent according to the average score. We study strategic agents whose objective is to be selected by the test. For simultaneous arm choices, we show that there exists a scoring test that successfully identifies the more-informed agent. For sequential arm choices, however, no such scoring test exists. Finally, we explore the tension between identifying the more-informed agent and maximizing welfare. A DM whose objective is to pass the test may not necessarily make welfare-maximizing decisions. In a binary-arm environment, we show that no scoring test can simultaneously identify the more informed agent and achieve more than half of the welfare attained by welfare-maximizing decisions.

cs.GT↗

arXiv2025

Efficiency in Games with Incomplete Information

We study games with incomplete information and characterize when a feasible outcome is Pareto efficient. Outcomes with excessive randomization are inefficient: generically, the total number of action profiles across states must be strictly less than the sum of the number of players and the number of states. We consider three applications. A cheap talk outcome is efficient only if pure; with state-independent sender payoffs, it is efficient if and only if the sender's most preferred action is induced with certainty. In natural settings, Bayesian persuasion outcomes are inefficient across many priors. Finally, ranking-based allocation mechanisms are inefficient under mild conditions.

econ.TH↗

arXiv2024

Persuading while Learning

We propose a dynamic product adoption persuasion model involving an impatient partially informed sender who gradually learns the state. In this model, the sender gathers information over time, and hence her posteriors' sequence forms a discrete-time martingale. The sender commits to a dynamic revelation policy to persuade the agent to adopt a product. We demonstrate that under the assumption that the sender's martingale possesses Blackwell-preserving kernels, the family of optimal strategies for the sender takes an interval form; namely, in every period the set of martingale realizations in which adoption occurs is an interval. Utilizing this, we prove that if the sender is sufficiently impatient, then under a random walk martingale, the optimal policy is fully transparent up to the moment of adoption; namely, the sender reveals the entire information she privately holds in every period.

cs.GT↗

arXiv2024

Robust Price Discrimination

We consider a model of third-degree price discrimination where the seller's product valuation is unknown to the market designer, who aims to maximize buyer surplus by revealing buyer valuation information. Our main result shows that the regret is bounded by a $\frac{1}{e}$-fraction of the optimal buyer surplus when the seller has zero valuation for the product. This bound is attained by randomly drawing a seller valuation and applying the segmentation of Bergemann et al. (2015) with respect to the drawn valuation. We show that this bound is tight in the case of binary buyer valuation.

econ.TH↗

arXiv2023

Fair Division via Quantile Shares

We consider the problem of fair division, where a set of indivisible goods should be distributed fairly among a set of agents with combinatorial valuations. To capture fairness, we adopt the notion of shares, where each agent is entitled to a fair share, based on some fairness criterion, and an allocation is considered fair if the value of every agent (weakly) exceeds her fair share. A share-based notion is considered universally feasible if it admits a fair allocation for every profile of monotone valuations. A major question arises: is there a non-trivial share-based notion that is universally feasible? The most well-known share-based notions, namely proportionality and maximin share, are not universally feasible, nor are any constant approximations of them. We propose a novel share notion, where an agent assesses the fairness of a bundle by comparing it to her valuation in a random allocation. In this framework, a bundle is considered $q$-quantile fair, for $q\in[0,1]$, if it is at least as good as a bundle obtained in a uniformly random allocation with probability at least $q$. Our main question is whether there exists a constant value of $q$ for which the $q$-quantile share is universally feasible. Our main result establishes a strong connection between the feasibility of quantile shares and the classical Erd\H{o}s Matching Conjecture. Specifically, we show that if a version of this conjecture is true, then the $\frac{1}{2e}$-quantile share is universally feasible. Furthermore, we provide unconditional feasibility results for additive, unit-demand and matroid-rank valuations for constant values of $q$. Finally, we discuss the implications of our results for other share notions.

cs.GT↗

arXiv2023

Algorithmic Cheap Talk

The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver's action by communicating a cheap talk message to the receiver. This paper initiates the systematic algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver's possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. We further prove that deciding whether there exists an equilibrium in which the receiver gets utility higher than the trivial utility he can guarantee is NP-hard. Fortunately, we identify two naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium - a constant number of states or a receiver having only two actions.

cs.GT↗

arXiv2023

Feasible Conditional Belief Distributions

Agents receive private signals about an unknown state. The resulting joint belief distributions are complex and lack a simple characterization. Our key insight is that, when conditioned on the state, the structure of belief distributions simplifies: feasibility constrains only the marginal distributions of individual agents across states, with no joint constraints within a state. We apply this insight to multi-receiver persuasion, identifying new tractable cases and introducing optimal transportation and duality tools.

econ.TH↗

arXiv2023

A Random Dictator Is All You Need

We study information aggregation with a decision maker aggregating binary recommendations from symmetric agents. Each agent's recommendation depends on her private information about a hidden state. While the decision maker knows the prior distribution over states and the marginal distribution of each agent's recommendation, the recommendations are adversarially-correlated. The decision maker's goal is choosing a robustly-optimal aggregation rule. We prove that for a large number of agents, for the three standard robustness paradigms - minimax, regret and approximation ratio - the unique optimal aggregation rule is random dictator. We further characterize the minimal regret for any agents' number through concavification.

cs.GT↗

arXiv2023

The Hazards and Benefits of Condescension in Social Learning

In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to worse outcomes, as does anti-condescension.

econ.TH↗

arXiv2022

Information Design in the Principal-Agent Problem

We study a variant of the principal-agent problem in which the principal does not directly observe the agent's effort outcome; rather, she gets a signal about the agent's action according to a variable information structure designed by a regulator. We consider both the case of a risk-neutral and of a risk-averse agent, focusing mainly on a setting with a limited liability assumption. We provide a clean characterization for implementability of actions and utility profiles by any information structure, which turns out to be simple thresholds on the utilities. We further study naturally constrained information structures in which the signal emitted from any action is either the action itself or some actions nearby. We show that the worst implementable welfare deteriorates gracefully as the information structure becomes noisier. Finally, we show that our clean characterization does not generalize to a larger class of signaling constraints. In fact, even deciding whether a certain action is implementable by some constrained information structure from this class is NP-complete in the general setting.

cs.GT↗

arXiv2022

Multi-Channel Bayesian Persuasion

The celebrated Bayesian persuasion model considers strategic communication between an informed agent (the sender) and uninformed decision makers (the receivers). The current rapidly-growing literature mostly assumes a dichotomy: either the sender is powerful enough to communicate separately with each receiver (a.k.a. private persuasion), or she cannot communicate separately at all (a.k.a. public persuasion). We study a model that smoothly interpolates between the two, by considering a natural multi-channel communication structure in which each receiver observes a subset of the sender's communication channels. This captures, e.g., receivers on a network, where information spillover is almost inevitable. We completely characterize when one communication structure is better for the sender than another, in the sense of yielding higher optimal expected utility universally over all prior distributions and utility functions. The characterization is based on a simple pairwise relation among receivers - one receiver information-dominates another if he observes at least the same channels. We prove that a communication structure $M_1$ is (weakly) better than $M_2$ if and only if every information-dominating pair of receivers in $M_1$ is also such in $M_2$. We also provide an additive FPTAS for the optimal sender's signaling scheme when the number of states is constant and the graph of information-dominating pairs is a directed forest. Finally, we prove that finding an optimal signaling scheme under multi-channel persuasion is, generally, computationally harder than under both public and private persuasion.

cs.GT↗

arXiv2022

Bayesian Persuasion with Mediators

An informed sender communicates with an uninformed receiver through a sequence of uninformed mediators; agents' utilities depend on receiver's action and the state. For any number of mediators, the sender's optimal value is characterized. For one mediator, the characterization has a geometric meaning of constrained concavification of sender's utility, optimal persuasion requires the same number of signals as without mediators, and the presence of the mediator is never profitable for the sender. Surprisingly, the second mediator may improve the value but optimal persuasion may require more signals.

econ.TH↗

arXiv2022

A Population's Feasible Posterior Beliefs

We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs in the population are feasible. We provide a necessary and sufficient condition for feasibility. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.

cs.GT↗

arXiv2021

Regret-Minimizing Bayesian Persuasion

We study a Bayesian persuasion setting with binary actions (adopt and reject) for Receiver. We examine the following question - how well can Sender perform, in terms of persuading Receiver to adopt, when ignorant of Receiver's utility? We take a robust (adversarial) approach to study this problem; that is, our goal is to design signaling schemes for Sender that perform well for all possible Receiver's utilities. We measure performance of signaling schemes via the notion of (additive) regret: the difference between Sender's hypothetically optimal utility had she known Receiver's utility function and her actual utility induced by the given scheme. On the negative side, we show that if Sender has no knowledge at all about Receiver's utility, then Sender has no signaling scheme that performs robustly well. On the positive side, we show that if Sender only knows Receiver's ordinal preferences of the states of nature - i.e., Receiver's utility upon adoption is monotonic as a function of the state - then Sender can guarantee a surprisingly low regret even when the number of states tends to infinity. In fact, we exactly pin down the minimum regret value that Sender can guarantee in this case, which turns out to be at most 1/e. We further show that such positive results are not possible under the alternative performance measure of a multiplicative approximation ratio by proving that no constant ratio can be guaranteed even for monotonic Receiver's utility; this may serve to demonstrate the merits of regret as a robust performance measure that is not too pessimistic. Finally, we analyze an intermediate setting in between the no-knowledge and the ordinal-knowledge settings.

cs.GT↗

arXiv2021

Bayesian Persuasion under Ex Ante and Ex Post Constraints

Bayesian persuasion is the study of information sharing policies among strategic agents. A prime example is signaling in online ad auctions: what information should a platform signal to an advertiser regarding a user when selling the opportunity to advertise to her? Practical considerations such as preventing discrimination, protecting privacy or acknowledging limited attention of the information receiver impose constraints on information sharing. In this work, we propose and analyze a simple way to mathematically model such constraints as restrictions on Receiver's admissible posterior beliefs. We consider two families of constraints - ex ante and ex post, where the latter limits each instance of Sender-Receiver communication, while the former more general family can also pose restrictions in expectation. For the ex ante family, Doval and Skreta establish the existence of an optimal signaling scheme with a small number of signals - at most the number of constraints plus the number of states of nature; we show this result is tight and provide an alternative proof for it. For the ex post family, we tighten a bound of Vølund, showing that the required number of signals is at most the number of states of nature, as in the original Kamenica-Gentzkow setting. As our main algorithmic result, we provide an additive bi-criteria FPTAS for an optimal constrained signaling scheme assuming a constant number of states; we improve the approximation to single-criteria under a Slater-like regularity condition. The FPTAS holds under standard assumptions; relaxed assumptions yield a PTAS. Finally, we bound the ratio between Sender's optimal utility under convex ex ante constraints and the corresponding ex post constraints. This bound applies to finding an approximately welfare-maximizing constrained signaling scheme in ad auctions.

cs.GT↗

arXiv2021

Settling the complexity of Nash equilibrium in congestion games

We consider (i) the problem of finding a (possibly mixed) Nash equilibrium in congestion games, and (ii) the problem of finding an (exponential precision) fixed point of the gradient descent dynamics of a smooth function $f:[0,1]^n \rightarrow \mathbb{R}$. We prove that these problems are equivalent. Our result holds for various explicit descriptions of $f$, ranging from (almost general) arithmetic circuits, to degree-$5$ polynomials. By a very recent result of [Fearnley, Goldberg, Hollender, Savani '20] this implies that these problems are PPAD$\cap$PLS-complete. As a corollary, we also obtain the following equivalence of complexity classes: CCLS = PPAD$\cap$PLS.

cs.CC↗

arXiv2021

Sequential Naive Learning

We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first forms her prior based on the aggregate statistic, then incorporates her signal with the prior based on Bayes rule, and finally applies a decision rule that assigns a (mixed) action to each belief. If priors are formed according to a discretized DeGroot rule, then actions converge to the state (in probability), i.e., \emph{asymptotic learning}, in any informative information structure if and only if the decision rule satisfies probability matching. This result generalizes to unspecified information settings where information structures differ across agents and agents know only the information structure generating their own signal. Also, the main result extends to the case of $n$ states and $n$ actions.

cs.LG↗

arXiv2020

Feasible Joint Posterior Beliefs

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of Aumann's Agreement Theorem, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995). For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

econ.TH↗