Related papers: Auctions and mass transportation
In this paper, we revisit the common claim that double auctions necessarily generate competitive equilibria. We begin by observing that competitive equilibrium has some counterintuitive implications: specifically, it predicts that monotone…
This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each…
The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
Transportation Network Companies employ dynamic pricing methods at periods of peak travel to incentivise driver participation and balance supply and demand for rides. Surge pricing multipliers are commonly used and are applied following…
Suppose that $c(x,y)$ is the cost of transporting a unit of mass from $x\in X$ to $y\in Y$ and suppose that a mass distribution $\mu$ on $X$ is transported optimally (so that the total cost of transportation is minimal) to the mass…
We study two standard multi-unit auction formats for allocating multiple units of a single good to multi-demand bidders. The first one is the Discriminatory Auction, which charges every winner his winning bids. The second is the Uniform…
We derive optimal strategies for a bidding agent that participates in multiple, simultaneous second-price auctions with perfect substitutes. We prove that, if everyone else bids locally in a single auction, the global bidder should always…
The Traveling Salesman Problem is a fundamental combinatorial optimization problem widely studied in operations research. Despite its simple formulation, it remains computationally challenging due to the exponential growth of the search…
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…
We propose a duality theory for multi-marginal repulsive cost that appear in optimal transport problems arising in Density Functional Theory. The related optimization problems involve probabilities on the entire space and, as minimizing…
We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide…
In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…
We study a repeated trading problem in which a mechanism designer facilitates trade between a single seller and multiple buyers. Our model generalizes the classic bilateral trade setting to a multi-buyer environment. Specifically, the…
Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem…
The Monge-Kantorovich problem for the infinite Wasserstein distance presents several peculiarities. Among them the lack of convexity and then of a direct duality. We study in dimension 1 the dual problem introduced by Barron, Bocea and…
The design of revenue-maximizing combinatorial auctions, i.e. multi-item auctions over bundles of goods, is one of the most fundamental problems in computational economics, unsolved even for two bidders and two items for sale. In the…
The issue of fairness in AI arises from discriminatory practices in applications like job recommendations and risk assessments, emphasising the need for algorithms that do not discriminate based on group characteristics. This concern is…
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…