Related papers: Auctions and mass transportation
We give a detailed review of two algorithms that solve the minimization case of the assignment problem. The Bertsekas' auction algorithm and the Goldberg & Kennedy algorithm. We will show that these algorithms are equivalent in the sense…
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this…
Matching problems have been widely studied in the research community, especially Ad-Auctions with many applications ranging from network design to advertising. Following the various advancements in machine learning, one natural question is…
We propose a uniform approach for the design and analysis of prior-free competitive auctions and online auctions. Our philosophy is to view the benchmark function as a variable parameter of the model and study a broad class of functions…
This paper slightly improves a classical result by Gangbo and McCann (1996) about the structure of optimal transport plans for costs that are concave functions of the Euclidean distance. Since the main difficulty for proving the existence…
We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved.…
The paper studies the problem of auction design in a setting where the auctioneer accesses the knowledge of the valuation distribution only through statistical samples. A new framework is established that combines the statistical decision…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
We prove the Duality Theorems for the stochastic optimal transportation problems with a convex cost function without a regularity assumption that is often supposed in the proof of the lower semicontinuity of an action integral. In our new…
The bi-objective winner determination problem (2WDP-SC) of a combinatorial procurement auction for transport contracts is characterized by a set B of bundle bids, with each bundle bid b in B consisting of a bidding carrier c_b, a bid price…
Motivated by sponsored search auctions, we study multi-unit auctions with budget constraints. In the mechanism we propose, Sort-Cut, understating budgets or values is weakly dominated. Since Sort-Cut's revenue is increasing in budgets and…
We provide simple and approximately revenue-optimal mechanisms in the multi-item multi-bidder settings. We unify and improve all previous results, as well as generalize the results to broader cases. In particular, we prove that the better…
Weak optimal transport has been recently introduced by Gozlan et al. The original motivation stems from the theory of geometric inequalities; further applications concern numerics of martingale optimal transport and stability in…
We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For…
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
We study the equilibria of uniform price auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds an equilibrium outcome as well as an…
Transit agencies have the opportunity to outsource certain services to established Mobility-on-Demand (MOD) providers. Such alliances can improve service quality, coverage, and ridership; reduce public sector costs and vehicular emissions;…
While auction theory views bids and valuations as continuous variables, real-world auctions are necessarily discrete. In this paper, we use a combination of analytical and computational methods to investigate whether incorporating…
Generating good revenue is one of the most important problems in Bayesian auction design, and many (approximately) optimal dominant-strategy incentive compatible (DSIC) Bayesian mechanisms have been constructed for various auction settings.…