A Double-Track Auction for Substitutes and Complements

We propose a new t^atonnement process called a double-track auction for efficiently allocating multiple heterogeneous indivisible items in two distinct sets S1 and S2 to many buyers who view items in the same set as substitutes but items across the two sets as complements. The auctioneer initially announces sufficiently low prices for items in one set, say S1, but sufficiently high prices for items in the other set S2. In each round, the buyers respond by reporting their demands at the current prices and the auctioneer adjusts prices upwards for items in S1 but downwards for items in S2 based on buyers' reported demands until the market is clear. Unlike any existing auction, this auction is a blend of a multi-item ascending auction and a multi-item descending auction. We prove that the auction finds an efficient allocation and its market-clearing prices in finitely many rounds. Based on the auction we also establish a dynamic, efficient and strategy-proof mechanism.Market design, dynamic auction, t^atonnement process, gross substitutes and complements, Walrasian equilibrium, incentives.

Collaborative Inference of Coexisting Information Diffusions

Recently, \textit{diffusion history inference} has become an emerging research topic due to its great benefits for various applications, whose purpose is to reconstruct the missing histories of information diffusion traces according to incomplete observations. The existing methods, however, often focus only on single information diffusion trace, while in a real-world social network, there often coexist multiple information diffusions over the same network. In this paper, we propose a novel approach called Collaborative Inference Model (CIM) for the problem of the inference of coexisting information diffusions. By exploiting the synergism between the coexisting information diffusions, CIM holistically models multiple information diffusions as a sparse 4th-order tensor called Coexisting Diffusions Tensor (CDT) without any prior assumption of diffusion models, and collaboratively infers the histories of the coexisting information diffusions via a low-rank approximation of CDT with a fusion of heterogeneous constraints generated from additional data sources. To improve the efficiency, we further propose an optimal algorithm called Time Window based Parallel Decomposition Algorithm (TWPDA), which can speed up the inference without compromise on the accuracy by utilizing the temporal locality of information diffusions. The extensive experiments conducted on real world datasets and synthetic datasets verify the effectiveness and efficiency of CIM and TWPDA

On Fair Allocations and Indivisibilities

This paper studies the problem of how to distribute a set of indivisible objects with an amount M of money among a number of agents in a fair way. We allow any number of agents and objects. Objects can be desirable or undesirable and the amount of money can be negative as well. In case M is negative, it can be regarded as costs to be shared by the agents. The objects with the money will be completely distributed among the agents in a way that each agent gets a bundle with at most one object if there are more agents than objects, and gets a bundle with at least one object if objects are no less than agents. We prove via an advanced fixed point argument that under rather mild and intuitive conditions the set of envy-free and efficient allocations is nonempty. Furthermore we demonstrate that if the total amount of money varies in an interval [X,Y], then there exists a connected set of fair allocations whose end points are allocations with sums of money equal to X and Y, respectively. Welfare properties are also analyzed when the total amount of money is modeled as a continuous variable. Our proof is based on a substantial generalization of the classic lemma of Knaster, Kuratowski and Mazurkewicz (KKM) in combinatorial topology.Indivisibility, fairness, Pareto optimality, resource allocation, multiperson decision, KKM lemma

Tail maximal dependence in bivariate models: estimation and applications

Assessing dependence within co-movements of financial instruments has been of much interest in risk management. Typically, indices of tail dependence are used to quantify the strength of such dependence, although many of the indices underestimate the strength. Hence, we advocate the use of a statistical procedure designed to estimate the maximal strength of dependence that can possibly occur among the co-movements. We illustrate the procedure using simulated and real data-sets