arXiv subjects

Nima Haghpanah

Publications and source records attributed to Nima Haghpanah.

10 recordsLinked to original sources

arXiv2026

Pay-Per-Crawl Pricing for AI: The LM-Tree Agent

As AI systems shift from directing users to content toward consuming it directly, publishers need a new revenue model: charging AI crawlers for content access. This model, called pay-per-crawl, must solve a problem of mechanism selection at scale: content is too heterogeneous for a fixed pricing framework. Different sub-types warrant not only different price levels but different pricing rules based on different unstructured features, and there are too many to enumerate or design by hand. We propose the LM Tree, an adaptive pricing agent that grows a segmentation tree over the content library, using LLMs to discover what distinguishes high-value from low-value items and apply those attributes at scale, from binary purchase feedback alone. We evaluate the LM Tree on real content from a major German technology publisher, using 8,939 articles and 80,451 buyer queries with willingness-to-pay calibrated from actual AI crawler traffic. The LM Tree achieves a 65% revenue gain over a single static price and a 47% gain over two-category pricing, outperforming even the publisher's own 8-segment editorial taxonomy by 40% -- recovering content distinctions the publisher's own categories miss.

econ.GN↗

arXiv2025

Good Data and Bad Data: The Welfare Effects of Price Discrimination

We study how a monopolist's use of consumer data for price discrimination affects welfare. To answer this question, we develop a model of market segmentation subject to residual uncertainty. We fully characterize when data usage monotonically increases or decreases welfare or when the effect is non-monotone. The characterization reduces the problem to one with only two demand curves, and gives a condition for the two-demand-curves case that highlights that information affects welfare in three distinct ways. In the non-monotone case, we provide tight bounds on the welfare effects of information and identify the best local direction for providing additional information.

econ.TH↗

arXiv2022

A Theory of Stable Market Segmentations

We consider a monopolistic seller in a market that may be segmented. The surplus of each consumer in a segment depends on the price that the seller optimally charges, which depends on the set of consumers in the segment. We study which segmentations may result from the interaction among consumers and the seller. Instead of studying the interaction as a non-cooperative game, we take a reduced-form approach and introduce a notion of stability that any resulting segmentation must satisfy. A stable segmentation is one that, for any alternative segmentation, contains a segment of consumers that prefers the original segmentation to the alternative one. Our main result characterizes stable segmentations as efficient and saturated. A segmentation is saturated if no consumers can be shifted from a segment with a high price to a segment with a low price without the seller optimally increasing the low price. We use this characterization to constructively show that stable segmentations always exist. Even though stable segmentations are efficient, they need not maximize average consumer surplus, and segmentations that maximize average consumer surplus need not be stable. Finally, we relate our notion of stability to solution concepts from cooperative game theory and show that stable segmentations satisfy many of them.

econ.TH↗

arXiv2020

How to Sell Hard Information

The seller of an asset has the option to buy hard information about the value of the asset from an intermediary. The seller can then disclose the acquired information before selling the asset in a competitive market. We study how the intermediary designs and sells hard information to robustly maximize her revenue across all equilibria. Even though the intermediary could use an accurate test that reveals the asset's value, we show that robust revenue maximization leads to a noisy test with a continuum of possible scores that are distributed exponentially. In addition, the intermediary always charges the seller for disclosing the test score to the market, but not necessarily for running the test. This enables the intermediary to robustly appropriate a significant share of the surplus resulting from the asset sale even though the information generated by the test provides no social value.

econ.TH↗

arXiv2017

Optimal Multi-Unit Mechanisms with Private Demands

In the multi-unit pricing problem, multiple units of a single item are for sale. A buyer's valuation for $n$ units of the item is $v \min \{ n, d\} $, where the per unit valuation $v$ and the capacity $d$ are private information of the buyer. We consider this problem in the Bayesian setting, where the pair $(v,d)$ is drawn jointly from a given probability distribution. In the \emph{unlimited supply} setting, the optimal (revenue maximizing) mechanism is a pricing problem, i.e., it is a menu of lotteries. In this paper we show that under a natural regularity condition on the probability distributions, which we call \emph{decreasing marginal revenue}, the optimal pricing is in fact \emph{deterministic}. It is a price curve, offering $i$ units of the item for a price of $p_i$, for every integer $i$. Further, we show that the revenue as a function of the prices $p_i$ is a \emph{concave} function, which implies that the optimum price curve can be found in polynomial time. This gives a rare example of a natural multi-parameter setting where we can show such a clean characterization of the optimal mechanism. We also give a more detailed characterization of the optimal prices for the case where there are only two possible demands.

cs.GT↗

arXiv2016

Sequential Mechanisms with ex-post Participation Guarantees

We provide a characterization of revenue-optimal dynamic mechanisms in settings where a monopolist sells k items over k periods to a buyer who realizes his value for item i in the beginning of period i. We require that the mechanism satisfies a strong individual rationality constraint, requiring that the stage utility of each agent be positive during each period. We show that the optimum mechanism can be computed by solving a nested sequence of static (single-period) mechanisms that optimize a tradeoff between the surplus of the allocation and the buyer's utility. We also provide a simple dynamic mechanism that obtains at least half of the optimal revenue. The mechanism either ignores history and posts the optimal monopoly price in each period, or allocates with a probability that is independent of the current report of the agent and is based only on previous reports. Our characterization extends to multi-agent auctions. We also formulate a discounted infinite horizon version of the problem, where we study the performance of "Markov mechanisms."

cs.GT↗

arXiv2015

Multi-dimensional Virtual Values and Second-degree Price Discrimination

We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing virtual values for multi-dimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts is not incentive compatible, and no general methodology is known for selecting the right paths for integration by parts. We resolve this issue by first uniquely solving for paths that satisfy certain necessary conditions that the pointwise optimality of the mechanism imposes on virtual values, and then identifying distributions that ensure the resulting virtual surplus is indeed pointwise optimized by the mechanism. Our method of solving for virtual values is general, and as a second application we use it to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences.

cs.GT↗

arXiv2014

Optimal Auctions for Correlated Buyers with Sampling

Crémer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Crémer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span.

cs.GT↗

arXiv2014

The Simple Economics of Approximately Optimal Auctions

The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with linear utility and single-dimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact optimizing marginal revenue. In particular Myerson's virtual values are exactly the derivative of an appropriate revenue curve. This paper considers mechanism design in environments where the agents have multi-dimensional and non-linear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal and there is sometimes no direct way to implement the marginal revenue maximization. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal (by identifying an important condition that we call revenue linearity), we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from ideal (where marginal revenue maximization is optimal). Because the marginal revenue mechanism is optimal for single-dimensional agents, our generalization immediately approximately extends many results for single-dimensional agents. One of the biggest open questions in Bayesian algorithmic mechanism design is developing methodologies that are not brute-force in the size of the agent type space. Our methods identify a subproblem that, e.g., for unit-demand agents with values drawn from product distributions, enables approximation mechanisms that are polynomial in the dimension.

cs.GT↗

arXiv2012

Bayesian Optimal Auctions via Multi- to Single-agent Reduction

We study an abstract optimal auction problem for a single good or service. This problem includes environments where agents have budgets, risk preferences, or multi-dimensional preferences over several possible configurations of the good (furthermore, it allows an agent's budget and risk preference to be known only privately to the agent). These are the main challenge areas for auction theory. A single-agent problem is to optimize a given objective subject to a constraint on the maximum probability with which each type is allocated, a.k.a., an allocation rule. Our approach is a reduction from multi-agent mechanism design problem to collection of single-agent problems. We focus on maximizing revenue, but our results can be applied to other objectives (e.g., welfare). An optimal multi-agent mechanism can be computed by a linear/convex program on interim allocation rules by simultaneously optimizing several single-agent mechanisms subject to joint feasibility of the allocation rules. For single-unit auctions, Border \citeyearpar{B91} showed that the space of all jointly feasible interim allocation rules for $n$ agents is a $\NumTypes$-dimensional convex polytope which can be specified by $2^\NumTypes$ linear constraints, where $\NumTypes$ is the total number of all agents' types. Consequently, efficiently solving the mechanism design problem requires a separation oracle for the feasibility conditions and also an algorithm for ex-post implementation of the interim allocation rules. We show that the polytope of jointly feasible interim allocation rules is the projection of a higher dimensional polytope which can be specified by only $O(\NumTypes^2)$ linear constraints. Furthermore, our proof shows that finding a preimage of the interim allocation rules in the higher dimensional polytope immediately gives an ex-post implementation.

cs.GT↗