Size versus truthfulness in the house allocation problem

We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of eovere-1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 18 over 13 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be non-bossy, an improved lower bound of eovere-1 holds. This lower bound is tight given that RSDM for strict preference lists is non-bossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants

Vickrey Auctions for Irregular Distributions

The classic result of Bulow and Klemperer \cite{BK96} says that in a single-item auction recruiting one more bidder and running the Vickrey auction achieves a higher revenue than the optimal auction's revenue on the original set of bidders, when values are drawn i.i.d. from a regular distribution. We give a version of Bulow and Klemperer's result in settings where bidders' values are drawn from non-i.i.d. irregular distributions. We do this by modeling irregular distributions as some convex combination of regular distributions. The regular distributions that constitute the irregular distribution correspond to different population groups in the bidder population. Drawing a bidder from this collection of population groups is equivalent to drawing from some convex combination of these regular distributions. We show that recruiting one extra bidder from each underlying population group and running the Vickrey auction gives at least half of the optimal auction's revenue on the original set of bidders

LP-based Covering Games with Low Price of Anarchy

We present a new class of vertex cover and set cover games. The price of anarchy bounds match the best known constant factor approximation guarantees for the centralized optimization problems for linear and also for submodular costs -- in contrast to all previously studied covering games, where the price of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In particular, we describe a vertex cover game with a price of anarchy of 2. The rules of the games capture the structure of the linear programming relaxations of the underlying optimization problems, and our bounds are established by analyzing these relaxations. Furthermore, for linear costs we exhibit linear time best response dynamics that converge to these almost optimal Nash equilibria. These dynamics mimic the classical greedy approximation algorithm of Bar-Yehuda and Even [3]

Absence of evidence of Xenotropic Murine Leukemia Virus-related virus infection in persons with Chronic Fatigue Syndrome and healthy controls in the United States

<p>Abstract</p> <p>Background</p> <p>XMRV, a xenotropic murine leukemia virus (MuLV)-related virus, was recently identified by PCR testing in 67% of persons with chronic fatigue syndrome (CFS) and in 3.7% of healthy persons from the United States. To investigate the association of XMRV with CFS we tested blood specimens from 51 persons with CFS and 56 healthy persons from the US for evidence of XMRV infection by using serologic and molecular assays. Blinded PCR and serologic testing were performed at the US Centers for Disease Control and Prevention (CDC) and at two additional laboratories.</p> <p>Results</p> <p>Archived blood specimens were tested from persons with CFS defined by the 1994 international research case definition and matched healthy controls from Wichita, Kansas and metropolitan, urban, and rural Georgia populations. Serologic testing at CDC utilized a Western blot (WB) assay that showed excellent sensitivity to MuLV and XMRV polyclonal or monoclonal antibodies, and no reactivity on sera from 121 US blood donors or 26 HTLV-and HIV-infected sera. Plasma from 51 CFS cases and plasma from 53 controls were all WB negative. Additional blinded screening of the 51 cases and 53 controls at the Robert Koch Institute using an ELISA employing recombinant Gag and Env XMRV proteins identified weak seroreactivity in one CFS case and a healthy control, which was not confirmed by immunofluorescence. PCR testing at CDC employed a <it>gag </it>and a <it>pol </it>nested PCR assay with a detection threshold of 10 copies in 1 ug of human DNA. DNA specimens from 50 CFS patients and 56 controls and 41 US blood donors were all PCR-negative. Blinded testing by a second nested gag PCR assay at the Blood Systems Research Institute was also negative for DNA specimens from the 50 CFS cases and 56 controls.</p> <p>Conclusions</p> <p>We did not find any evidence of infection with XMRV in our U.S. study population of CFS patients or healthy controls by using multiple molecular and serologic assays. These data do not support an association of XMRV with CFS.</p

Truthful Mechanism Design for Multidimensional Covering Problems

We investigate multidimensional covering mechanism-design problems, wherein there are m items that need to be covered and n agents who provide covering objects, with each agent i having a private cost for the covering objects he provides. The goal is to select a set of covering objects of minimum total cost that together cover all the items. We focus on two representative covering problems: uncapacitated facility location (UFL) and vertex cover (VC). For multidimensional UFL, we give a black-box method to transform any Lagrangian-multiplier-preserving ρ-approximation algorithm for UFL to a truthful-in-expectation, ρ-approx. mechanism. This yields the first result for multidimensional UFL, namely a truthful-in-expectation 2-approximation mechanism. For multidimensional VC (Multi-VC), we develop a decomposition method that reduces the mechanism-design problem into the simpler task of constructing threshold mechanisms, which are a restricted class of truthful mechanisms, for simpler (in terms of graph structure or problem dimension) instances of Multi-VC. By suitably designing the decomposition and the threshold mechanisms it uses as building blocks, we obtain truthful mechanisms with approximation ratios (n is the number of nodes): (1) O(log n) for Multi-VC on any minor-closed family of graphs; and (2) O(r 2 log n) for r-dimensional VC on any graph. These are the first truthful mechanisms for Multi-VC with non-trivial approximation guarantees

Non-cooperative facility location and covering games

Abstract. We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation. Each player wants to satisfy a subset of the constraints. Variables represent resources, which are available in costly integer units and must be bought. The cost can be shared arbitrarily between players. Once a unit is bought, it can be used by all players to satisfy their constraints. In general the cost of pure-strategy Nash equilibria in this game can be prohibitively high, as both prices of anarchy and stability are in Θ(k). In addition, deciding the existence of pure Nash equilibria is NP-hard. These results extend to recently studied single-source connection games. Under certain conditions, however, cheap Nash equilibria exist: if the integrality gap of the underlying integer program is 1 and in the case of single constraint players. In addition, we present algorithms that compute cheap approximate Nash equilibria in polynomial time.