arXiv subjects

Reza Alijani

Publications and source records attributed to Reza Alijani.

3 recordsLinked to original sources

arXiv2022

The Limits of an Information Intermediary in Auction Design

We study the limits of an information intermediary in the classical Bayesian auction, where a revenue-maximizing seller sells one item to $n$ buyers with independent private values. In addition, we have an intermediary who knows the buyers' private values, and can map these to a public signal so as to increase consumer surplus. This model generalizes the single-buyer setting proposed by Bergemann, Brooks, and Morris, who present a signaling scheme that raises the optimal consumer surplus, by guaranteeing that the item is always sold and the seller gets the same revenue as without signaling. Our work aims to understand how this result ports to the setting with multiple buyers. We likewise define the benchmark for the optimal consumer surplus: one where the auction is efficient (i.e., the item is always sold to the highest-valued buyer) and the revenue of the seller is unchanged. We show that no signaling scheme can guarantee this benchmark even for $n=2$ buyers with $2$-point valuation distributions. Indeed, no signaling scheme can be efficient while preserving any non-trivial fraction of the original consumer surplus, and no signaling scheme can guarantee consumer surplus better than a factor of $\frac{1}{2}$ compared to the benchmark. These impossibility results are existential (beyond computational), and provide a sharp separation between the single and multi-buyer settings. In light of this impossibility, we develop signaling schemes with good approximation guarantees to the benchmark. Our main technical result is an $O(1)$-approximation for i.i.d. regular buyers, via signaling schemes that are conceptually simple and computable in polynomial time. We also present an extension to the case of general independent distributions.

cs.GT↗

arXiv2020

Predict and Match: Prophet Inequalities with Uncertain Supply

We consider the problem of selling perishable items to a stream of buyers in order to maximize social welfare. A seller starts with a set of identical items, and each arriving buyer wants any one item, and has a valuation drawn i.i.d. from a known distribution. Each item, however, disappears after an a priori unknown amount of time that we term the horizon for that item. The seller knows the (possibly different) distribution of the horizon for each item, but not its realization till the item actually disappears. As with the classic prophet inequalities, the goal is to design an online pricing scheme that competes with the prophet that knows the horizon and extracts full social surplus (or welfare). Our main results are for the setting where items have independent horizon distributions satisfying the monotone-hazard-rate (MHR) condition. Here, for any number of items, we achieve a constant-competitive bound via a conceptually simple policy that balances the rate at which buyers are accepted with the rate at which items are removed from the system. We implement this policy via a novel technique of matching via probabilistically simulating departures of the items at future times. Moreover, for a single item and MHR horizon distribution with mean $μ$, we show a tight result: There is a fixed pricing scheme that has competitive ratio at most $2 - 1/μ$, and this is the best achievable in this class. We further show that our results are best possible. First, we show that the competitive ratio is unbounded without the MHR assumption even for one item. Further, even when the horizon distributions are i.i.d. MHR and the number of items becomes large, the competitive ratio of any policy is lower bounded by a constant greater than $1$, which is in sharp contrast to the setting with identical deterministic horizons.

cs.GT↗

arXiv2018

Two-sided Facility Location

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. Motivated by these platforms, we formulate a set of facility location problems that we term Two-sided Facility location. In our model, agents arrive at nodes in an underlying metric space, where the metric distance between any buyer and seller captures the quality of the corresponding match. The platform posts prices and wages at the nodes, and opens a set of facilities to route the agents to. The agents at any facility are assumed to be matched. The platform ensures high match quality by imposing a distance constraint between a node and the facilities it is routed to. It ensures high service availability by ensuring flow to the facility is at least a pre-specified lower bound. Subject to these constraints, the goal of the platform is to maximize the social surplus (or gains from trade) subject to weak budget balance, i.e., profit being non-negative. We present an approximation algorithm for this problem that yields a $(1 + ε)$ approximation to surplus for any constant $ε> 0$, while relaxing the match quality (i.e., maximum distance of any match) by a constant factor. We use an LP rounding framework that easily extends to other objectives such as maximizing volume of trade or profit. We justify our models by considering a dynamic marketplace setting where agents arrive according to a stochastic process and have finite patience (or deadlines) for being matched. We perform queueing analysis to show that for policies that route agents to facilities and match them, ensuring a low abandonment probability of agents reduces to ensuring sufficient flow arrives at each facility.

cs.GT↗