arXiv subjects

Jason D. Hartline

Publications and source records attributed to Jason D. Hartline.

At least 19 recordsLinked to original sources

arXiv2026

The Computable but Not Learnable Information-Value-Free Equilibria and Regulation of Algorithmic Collusion

A correlated equilibrium is information-value-free if every player has an action that yields the same payoff as their equilibrium strategy when all other players follow their respective equilibrium strategies. An equilibrium is learnable if the empirical history of play generated by certain learning algorithms using only full feedback on each player's own payoff converges to it. Our main result is that although an information-value-free equilibrium can be computed efficiently offline, it is not learnable by a broad class of learning algorithms. This separation stands in sharp contrast to canonical equilibrium concepts, where offline computation and online learning typically have comparable difficulty. In information-economics terms, our results imply that learning correlated equilibria in games cannot avoid generating valuable information, which has implications for current debates on the regulation of algorithmic collusion: Valuable and implicit information exchange is unavoidable under rationalizable learning, and traditional antitrust regulation against such exchange is therefore incompatible with rationalizable learning. Our results also imply an informational impossibility result for time-average convergence to a Nash equilibrium by a broad class of learning algorithms.

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arXiv2025

Regulation of Algorithmic Collusion, Refined: Testing Pessimistic Calibrated Regret

We study the regulation of algorithmic (non-)collusion amongst sellers in dynamic imperfect price competition by auditing their data as introduced by Hartline et al. [2024]. We develop an auditing method that tests whether a seller's pessimistic calibrated regret is low. The pessimistic calibrated regret is the highest calibrated regret of outcomes compatible with the observed data. This method relaxes the previous requirement that a pricing algorithm must use fully-supported price distributions to be auditable. This method is at least as permissive as any auditing method that has a high probability of failing algorithmic outcomes with non-vanishing calibrated regret. Additionally, we strengthen the justification for using vanishing calibrated regret, versus vanishing best-in-hindsight regret, as the non-collusion definition, by showing that even without any side information, the pricing algorithms that only satisfy weaker vanishing best-in-hindsight regret allow an opponent to manipulate them into posting supra-competitive prices. This manipulation cannot be excluded with a non-collusion definition of vanishing best-in-hindsight regret. We motivate and interpret the approach of auditing algorithms from their data as suggesting a per se rule. However, we demonstrate that it is possible for algorithms to pass the audit by pretending to have higher costs than they actually do. For such scenarios, the rule of reason can be applied to bound the range of costs to those that are reasonable for the domain.

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arXiv2024

Algorithmic Robust Forecast Aggregation

Forecast aggregation combines the predictions of multiple forecasters to improve accuracy. However, the lack of knowledge about forecasters' information structure hinders optimal aggregation. Given a family of information structures, robust forecast aggregation aims to find the aggregator with minimal worst-case regret compared to the omniscient aggregator. Previous approaches for robust forecast aggregation rely on heuristic observations and parameter tuning. We propose an algorithmic framework for robust forecast aggregation. Our framework provides efficient approximation schemes for general information aggregation with a finite family of possible information structures. In the setting considered by Arieli et al. (2018) where two agents receive independent signals conditioned on a binary state, our framework also provides efficient approximation schemes by imposing Lipschitz conditions on the aggregator or discrete conditions on agents' reports. Numerical experiments demonstrate the effectiveness of our method by providing a nearly optimal aggregator in the setting considered by Arieli et al. (2018).

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arXiv2024

Error-Tolerant E-Discovery Protocols

We consider the multi-party classification problem introduced by Dong, Hartline, and Vijayaraghavan (2022) in the context of electronic discovery (e-discovery). Based on a request for production from the requesting party, the responding party is required to provide documents that are responsive to the request except for those that are legally privileged. Our goal is to find a protocol that verifies that the responding party sends almost all responsive documents while minimizing the disclosure of non-responsive documents. We provide protocols in the challenging non-realizable setting, where the instance may not be perfectly separated by a linear classifier. We demonstrate empirically that our protocol successfully manages to find almost all relevant documents, while incurring only a small disclosure of non-responsive documents. We complement this with a theoretical analysis of our protocol in the single-dimensional setting, and other experiments on simulated data which suggest that the non-responsive disclosure incurred by our protocol may be unavoidable.

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arXiv2024

Regulation of Algorithmic Collusion

Consider sellers in a competitive market that use algorithms to adapt their prices from data that they collect. In such a context it is plausible that algorithms could arrive at prices that are higher than the competitive prices and this may benefit sellers at the expense of consumers (i.e., the buyers in the market). This paper gives a definition of plausible algorithmic non-collusion for pricing algorithms. The definition allows a regulator to empirically audit algorithms by applying a statistical test to the data that they collect. Algorithms that are good, i.e., approximately optimize prices to market conditions, can be augmented to contain the data sufficient to pass the audit. Algorithms that have colluded on, e.g., supra-competitive prices cannot pass the audit. The definition allows sellers to possess useful side information that may be correlated with supply and demand and could affect the prices used by good algorithms. The paper provides an analysis of the statistical complexity of such an audit, i.e., how much data is sufficient for the test of non-collusion to be accurate.

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arXiv2023

Optimal Scoring Rules for Multi-dimensional Effort

This paper develops a framework for the design of scoring rules to optimally incentivize an agent to exert a multi-dimensional effort. This framework is a generalization to strategic agents of the classical knapsack problem (cf. Briest, Krysta, and Vöcking, 2005, Singer, 2010) and it is foundational to applying algorithmic mechanism design to the classroom. The paper identifies two simple families of scoring rules that guarantee constant approximations to the optimal scoring rule. The truncated separate scoring rule is the sum of single dimensional scoring rules that is truncated to the bounded range of feasible scores. The threshold scoring rule gives the maximum score if reports exceed a threshold and zero otherwise. Approximate optimality of one or the other of these rules is similar to the bundling or selling separately result of Babaioff, Immorlica, Lucier, and Weinberg (2014). Finally, we show that the approximate optimality of the best of those two simple scoring rules is robust when the agent's choice of effort is made sequentially.

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arXiv2022

Algorithmic Learning Foundations for Common Law

This paper looks at a common law legal system as a learning algorithm, models specific features of legal proceedings, and asks whether this system learns efficiently. A particular feature of our model is explicitly viewing various aspects of court proceedings as learning algorithms. This viewpoint enables directly pointing out that when the costs of going to court are not commensurate with the benefits of going to court, there is a failure of learning and inaccurate outcomes will persist in cases that settle. Specifically, cases are brought to court at an insufficient rate. On the other hand, when individuals can be compelled or incentivized to bring their cases to court, the system can learn and inaccuracy vanishes over time.

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arXiv2022

Mechanism Redesign

This paper develops the theory of mechanism redesign by which an auctioneer can reoptimize an auction based on bid data collected from previous iterations of the auction on bidders from the same market. We give a direct method for estimation of the revenue of a counterfactual auction from the bids in the current auction. The estimator is a simple weighted order statistic of the bids and has the optimal error rate. Two applications of our estimator are A/B testing (a.k.a., randomized controlled trials) and instrumented optimization (i.e., revenue optimization subject to being able to do accurate inference of any counterfactual auction revenue).

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arXiv2021

Revelation Gap for Pricing from Samples

This paper considers prior-independent mechanism design, in which a single mechanism is designed to achieve approximately optimal performance on every prior distribution from a given class. Most results in this literature focus on mechanisms with truthtelling equilibria, a.k.a., truthful mechanisms. Feng and Hartline (2018) introduce the revelation gap to quantify the loss of the restriction to truthful mechanisms. We solve a main open question left in Feng and Hartline (2018); namely, we identify a non-trivial revelation gap for revenue maximization. Our analysis focuses on the canonical problem of selling a single item to a single agent with only access to a single sample from the agent's valuation distribution. We identify the sample-bid mechanism (a simple non-truthful mechanism) and upper-bound its prior-independent approximation ratio by 1.835 (resp. 1.296) for regular (resp. MHR) distributions. We further prove that no truthful mechanism can achieve prior-independent approximation ratio better than 1.957 (resp. 1.543) for regular (resp. MHR) distributions. Thus, a non-trivial revelation gap is shown as the sample-bid mechanism outperforms the optimal prior-independent truthful mechanism. On the hardness side, we prove that no (possibly non-truthful) mechanism can achieve prior-independent approximation ratio better than 1.073 even for uniform distributions.

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arXiv2020

Optimal Auctions vs. Anonymous Pricing: Beyond Linear Utility

The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymous pricing for regular agents approximately extends to agents that satisfy this approximate regularity property. We apply this approximation framework to prove that anonymous pricing is a constant approximation to the revenue optimal single-item auction for agents with public-budget utility, private-budget utility, and (a special case of) risk-averse utility.

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arXiv2020

Optimization of Scoring Rules

We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional problems, and choose the dimension with the most surprising signal to be scored on in symmetric multi-dimensional problems. This scoring rule format remains approximately optimal for asymmetric distributions. These results demonstrate the importance of linking incentives to obtain high-quality information in multi-dimensional problems. In contrast, standard scoring rules like the quadratic scoring rule, or averages of single-dimensional scoring rules can be far from optimal.

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arXiv2020

A Truthful Cardinal Mechanism for One-Sided Matching

We revisit the well-studied problem of designing mechanisms for one-sided matching markets, where a set of $n$ agents needs to be matched to a set of $n$ heterogeneous items. Each agent $i$ has a value $v_{i,j}$ for each item $j$, and these values are private information that the agents may misreport if doing so leads to a preferred outcome. Ensuring that the agents have no incentive to misreport requires a careful design of the matching mechanism, and mechanisms proposed in the literature mitigate this issue by eliciting only the \emph{ordinal} preferences of the agents, i.e., their ranking of the items from most to least preferred. However, the efficiency guarantees of these mechanisms are based only on weak measures that are oblivious to the underlying values. In this paper we achieve stronger performance guarantees by introducing a mechanism that truthfully elicits the full \emph{cardinal} preferences of the agents, i.e., all of the $v_{i,j}$ values. We evaluate the performance of this mechanism using the much more demanding Nash bargaining solution as a benchmark, and we prove that our mechanism significantly outperforms all ordinal mechanisms (even non-truthful ones). To prove our approximation bounds, we also study the population monotonicity of the Nash bargaining solution in the context of matching markets, providing both upper and lower bounds which are of independent interest.

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arXiv2018

An End-to-end Argument in Mechanism Design (Prior-independent Auctions for Budgeted Agents)

This paper considers prior-independent mechanism design, namely identifying a single mechanism that has near optimal performance on every prior distribution. We show that mechanisms with truthtelling equilibria, a.k.a., revelation mechanisms, do not always give optimal prior-independent mechanisms and we define the revelation gap to quantify the non-optimality of revelation mechanisms. This study suggests that it is important to develop a theory for the design of non-revelation mechanisms. Our analysis focuses on welfare maximization in single-item auctions for agents with budgets and a natural regularity assumption on their distribution of values. The all-pay auction (a non-revelation mechanism) is the Bayesian optimal mechanism; as it is prior-independent it is also the prior-independent optimal mechanism (a 1-approximation). We prove a lower bound on the prior-independent approximation of revelation mechanisms of 1.013 and that the clinching auction (a revelation mechanism) is a prior-independent $e \approx 2.714$ approximation. Thus the revelation gap for single-item welfare maximization with public budget agents is in $[1.013, e]$. Some of our analyses extend to the revenue objective, position environments, and irregular distributions.

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arXiv2016

A/B Testing of Auctions

For many application areas A/B testing, which partitions users of a system into an A (control) and B (treatment) group to experiment between several application designs, enables Internet companies to optimize their services to the behavioral patterns of their users. Unfortunately, the A/B testing framework cannot be applied in a straightforward manner to applications like auctions where the users (a.k.a., bidders) submit bids before the partitioning into the A and B groups is made. This paper combines auction theoretic modeling with the A/B testing framework to develop methodology for A/B testing auctions. The accuracy of our method %, assuming the auction is directly comparable to ideal A/B testing where there is no interference between A and B. Our results are based on an extension and improved analysis of the inference method of Chawla et al. (2014).

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arXiv2015

Bayesian Budget Feasibility with Posted Pricing

We consider the problem of budget feasible mechanism design proposed by Singer (2010), but in a Bayesian setting. A principal has a public value for hiring a subset of the agents and a budget, while the agents have private costs for being hired. We consider both additive and submodular value functions of the principal. We show that there are simple, practical, ex post budget balanced posted pricing mechanisms that approximate the value obtained by the Bayesian optimal mechanism that is budget balanced only in expectation. A main motivating application for this work is the crowdsourcing large projects, e.g., on Mechanical Turk, where workers are drawn from a large population and posted pricing is standard. Our analysis methods relate to contention resolution schemes in submodular optimization of Vondrak et al. (2011) and the correlation gap analysis of Yan (2011).

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arXiv2014

Optimal Platform Design

An auction house cannot generally provide the optimal auction technology to every client. Instead it provides one or several auction technologies, and clients select the most appropriate one. For example, eBay provides ascending auctions and "buy-it-now" pricing. For each client the offered technology may not be optimal, but it would be too costly for clients to create their own. We call these mechanisms, which emphasize generality rather than optimality, platform mechanisms. A platform mechanism will be adopted by a client if its performance exceeds that of the client's outside option, e.g., hiring (at a cost) a consultant to design the optimal mechanism. We ask two related questions. First, for what costs of the outside option will the platform be universally adopted? Second, what is the structure of good platform mechanisms? We answer these questions using a novel prior-free analysis framework in which we seek mechanisms that are approximately optimal for every prior.

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arXiv2013

Prior-Independent Mechanisms for Scheduling

We study the makespan minimization problem with unrelated selfish machines under the assumption that job sizes are stochastic. We design simple truthful mechanisms that under various distributional assumptions provide constant and sublogarithmic approximations to expected makespan. Our mechanisms are prior-independent in that they do not rely on knowledge of the job size distributions. Prior-independent approximation mechanisms have been previously studied for the objective of revenue maximization [Dhangwatnotai, Roughgarden and Yan'10, Devanur, Hartline, Karlin and Nguyen'11, Roughgarden, Talgam-Cohen and Yan'12]. In contrast to our results, in prior-free settings no truthful anonymous deterministic mechanism for the makespan objective can provide a sublinear approximation [Ashlagi, Dobzinski and Lavi'09].

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arXiv2012

Prior-free Auctions for Budgeted Agents

We consider prior-free auctions for revenue and welfare maximization when agents have a common budget. The abstract environments we consider are ones where there is a downward-closed and symmetric feasibility constraint on the probabilities of service of the agents. These environments include position auctions where slots with decreasing click-through rates are auctioned to advertisers. We generalize and characterize the envy-free benchmark from Hartline and Yan (2011) to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue. We give prior-free mechanisms that approximate these benchmarks. A building block in our mechanism is a clinching auction for position auction environments. This auction is a generalization of the multi-unit clinching auction of Dobzinski et al. (2008) and a special case of the polyhedral clinching auction of Goel et al. (2012). For welfare maximization, we show that this clinching auction is a good approximation to the envy-free optimal welfare for position auction environments. For profit maximization, we generalize the random sampling profit extraction auction from Fiat et al. (2002) for digital goods to give a 10.0-approximation to the envy-free optimal revenue in symmetric, downward-closed environments. The profit maximization question is of interest even without budgets and our mechanism is a 7.5-approximation which improving on the 30.4 bound of Ha and Hartline (2012).

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