Related papers: Auctions and mass transportation
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of --…
The current art in optimal combinatorial auctions is limited to handling the case of single units of multiple items, with each bidder bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an…
A convex duality result for martingale optimal transport problems with two marginals was established in Beiglb\"ock et al. (2013). In this paper we provide a generalization of this result to the multi-period setting.
We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a…
In this paper, we study sequential auctions with two budget constrained bidders and any number of identical items. All prior results on such auctions consider only two items. We construct a canonical outcome of the auction that is the only…
We consider auction environments in which at the time of the auction bidders observe signals about their ex-post value. We introduce a model of novice bidders who do not know know the joint distribution of signals and instead build a…
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
We study a seller who sells a single good to multiple bidders with uncertainty over the joint distribution of bidders' valuations, as well as bidders' higher-order beliefs about their opponents. The seller only knows the (possibly…
This letter considers the design of an auction mechanism to sell the object of a seller when the buyers quantize their private value estimates regarding the object prior to communicating them to the seller. The designed auction mechanism…
Most modern ticketing systems rely on a first-come-first-serve or randomized allocation system to determine the allocation of tickets. Such systems has received considerable backlash in recent years due to its inequitable allotment and…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
While the auto-bidding literature predominantly considers independent bidding, we investigate the coordination problem among multiple auto-bidders in online advertising platforms. Two motivating scenarios are: collaborative bidding among…
Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the…
We shall present a measure theoretical approach for which together with the Kantorovich duality provide an efficient tool to study the optimal transport problem. Specifically, we study the support of optimal plans where the cost function…
In this paper, we want to establish some general results in the Lorentzian optimal transport theory that have well-known Riemannian counterparts. As a first result, we will provide non-trivial assumptions on the measures to ensure strong…
We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an…
The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.
Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later a full analytical understanding of…
This is our first paper on the extension of our recent work on the Lax-Oleinik commutators and its applications to the intrinsic approach of propagation of singularities of the viscosity solutions of Hamilton-Jacobi equations. We…
This paper examines knapsack auctions as a method to solve the knapsack problem with incomplete information, where object values are private and sizes are public. We analyze three auction types-uniform price (UP), discriminatory price (DP),…