相关论文: Product-Mix Auctions and Tropical Geometry
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…
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when the cost function is smooth and the landscapes containing…
We define a congruence module $\Psi_A(M)$ associated to a surjective $\mathcal O$-algebra morphism $\lambda\colon A \to \mathcal{O}$, with $\mathcal{O}$ a discrete valuation ring, $A$ a complete noetherian local $\mathcal{O}$-algebra…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…
We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…
The Hitchin-Kobayashi correspondence for vector bundles, established by Donaldson, Kobayashi, Luebke, Uhlenbeck and Yau, states that an indecomposable holomorphic vector bundle over a compact Kaehler manifold is stable in the sense of…
The rise of the machine learning (ML) model economy has intertwined markets for training datasets and pre-trained models. However, most pricing approaches still separate data and model transactions or rely on broker-centric pipelines that…
In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces.…
The problem of allocating scarce items to individuals is an important practical question in market design. An increasingly popular set of mechanisms for this task uses the concept of market equilibrium: individuals report their preferences,…
In additive combinatorics, Erd\"{o}s-Szemer\'{e}di Conjecture is an important conjecture. It can be applied to many fields, such as number theory, harmonic analysis, incidence geometry, and so on. Additionally, its statement is quite easy…
We discuss bundle auctions within the framework of an integer allocation problem. We show that for multi-unit auctions, of which bundle auctions are a special case, market equilibrium and constrained market equilibrium are equivalent…
The problem of arriving at a principled method of pricing goods and services was very satisfactorily solved for conventional goods; however, this solution is not applicable to digital goods. This paper studies pricing of a special class of…
The notion of a tropical vector bundle on a toric variety was recently introduced by Khan-Maclagan and Kaveh-Manon. In this paper, we study the Euler characteristic and rank of global sections for tropical vector bundles. We associate a…
Recently Guillemin gave an explicit combinatorial way of constructing "toric" Kahler metrics on (symplectic) toric varieties, using only data on the moment polytope. In this paper, differential geometric properties of these metrics are…
This paper analyzes a steady state matching model interrelating the education and labor sectors. In this model, a heterogeneous population of students match with teachers to enhance their cognitive skills. As adults, they then choose to…
The well-known Constantin-Lax-Majda (CLM) equation, an important toy model of the 3D Euler equations without convection, can develop finite time singularities [5]. De Gregorio modified the CLM model by adding a convective term [6], which is…
We consider fundamental questions of arbitrage pricing arising when the uncertainty model is given by a set of possible mutually singular probability measures. With a single probability model, essential equivalence between the absence of…
In [1] we presented a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we were able to redefine concepts like account balance, yield…
We provide a new, much simplified and straightforward proof to a result of Pavlov [2011] regarding the revenue maximizing mechanism for selling two goods with uniformly i.i.d. valuations over intervals $[c,c+1]$, to an additive buyer. This…