Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

Online Set Cover with Set Requests

We consider a generic online allocation problem that generalizes the classical online set cover framework by considering requests comprising a set of elements rather than a single element. This problem has multiple applications in cloud computing, crowd sourcing, facility planning, etc. Formally, it is an online covering problem where each online step comprises an offline covering problem. In addition, the covering sets are capacitated, leading to packing constraints. We give a randomized algorithm for this problem that has a nearly tight competitive ratio in both objectives: overall cost and maximum capacity violation. Our main technical tool is an online algorithm for packing/covering LPs with nested constraints, which may be of interest in other applications as well

Revenue Maximization in Transportation Networks

We study the joint optimization problem of pricing trips in a transportation network and serving the induced demands by routing a fleet of available service vehicles to maximize revenue. Our framework encompasses applications that include traditional transportation networks (e.g., airplanes, buses) and their more modern counterparts (e.g., ride-sharing systems). We describe a simple combinatorial model, in which each edge in the network is endowed with a curve that gives the demand for traveling between its endpoints at any given price. We are supplied with a number of vehicles and a time budget to serve the demands induced by the prices that we set, seeking to maximize revenue. We first focus on a (preliminary) special case of our model with unit distances and unit time horizon. We show that this version of the problem can be solved optimally in polynomial time. Switching to the general case of our model, we first present a two-stage approach that separately optimizes for prices and routes, achieving a logarithmic approximation to revenue in the process. Next, using the insights gathered in the first two results, we present a constant factor approximation algorithm that jointly optimizes for prices and routes for the supply vehicles. Finally, we discuss how our algorithms can handle capacitated vehicles, impatient demands, and selfish (wage-maximizing) drivers

Optimal Design of Brushless Doubly Fed Reluctance Machine

Optimization techniques are widely used in the design of electrical machines to obtain maximum performance at minimal capital cost. After a brief overview of some of the optimization techniques employed in electrical machine design, this chapter highlights the features of brushless doubly fed reluctance machine (BDFRM) and its optimal design. The simple and robust construction, variable speed operation, better performance compared to traditional counterpart, and requirement of partially rated converter for speed control have made BDFRM an attractive alternative for variable speed applications such as pumps, blower, and wind generators. Due to unusual construction of BDFRM, conventional design procedures cannot be applied. A few critical issues in the design of BDFRM that greatly affect its performance are discussed. Design optimization is performed using nonlinear programming technique for 6-4-2 pole reluctance rotor and 8-6-4 pole ducted rotor configurations of BDFRM. 2 kW prototypes are then constructed for laboratory use. The performance of the prototypes is examined through finite element analysis (FEA) employing Maxwell 16 software. The test results are also presented

Structure of Polyethylene Prepared Between Non Metallic Electrodes

The X-Ray diffraction method has been applied to study the structural changes that polyethylene may undergo when prepared between glass and perspex electrodes at different temperatures. The results indicate that polyethylene does not undergo any considerable structural change under the prevailing conditions

Evaluation of treatment outcome of tuberculosis patients in the urban field practice area of D. Y. Patil Medical College, Pimpri, Pune

Background: Tuberculosis (TB) bacilli have lived in symbiosis with mankind since time immemorial. RNTCP is the largest and the fastest expanding programme throughout the world as 1.29 million patients in 2005, 1.39 million patients in 2006 and 1.48 million patients in 2007 were enrolled for treatment. In 2008, 1.51 million patients have already been placed on treatment. Treatment success rates have tripled from 25% to 86% & TB death rates have been cut 7 fold from 29% to 4% in comparison to the pre-RNTCP (Revised National Tuberculosis Control Programme) era.[1] Objective: To study treatment outcome in the form of cure rate, treatment completion rate, failure rate, death rate in the study area. Method: An ambispective study was done in urban field practice area attached to Padamshree Dr. D.Y. Patil Medical College Pimpri, Pune. The study was carried out during 1st July 2011 - 30th September 2013. Results: A total 429 subjects were enrolled in the study of which, 224(52.24%) were successfully completed the treatment, followed by 110(25.54%) which were cured, 34(07.92%) were defaulted, 28(06.52%) were transferred out, 17(03.96%) died and 16(03.72%) underwent treatment failure during the study period. Conclusion: In spite, of many efforts by RNTCP to treat tuberculosis patients it was found only 50 % of the subjects successfully completed the treatment

Maximizing Revenue in the Presence of Intermediaries

We study the mechanism design problem of selling $k$ items to unit-demand buyers with private valuations for the items. A buyer either participates directly in the auction or is represented by an intermediary, who represents a subset of buyers. Our goal is to design robust mechanisms that are independent of the demand structure (i.e. how the buyers are partitioned across intermediaries), and perform well under a wide variety of possible contracts between intermediaries and buyers. We first study the case of $k$ identical items where each buyer draws its private valuation for an item i.i.d. from a known $\lambda$-regular distribution. We construct a robust mechanism that, independent of the demand structure and under certain conditions on the contracts between intermediaries and buyers, obtains a constant factor of the revenue that the mechanism designer could obtain had she known the buyers' valuations. In other words, our mechanism's expected revenue achieves a constant factor of the optimal welfare, regardless of the demand structure. Our mechanism is a simple posted-price mechanism that sets a take-it-or-leave-it per-item price that depends on $k$ and the total number of buyers, but does not depend on the demand structure or the downstream contracts. Next we generalize our result to the case when the items are not identical. We assume that the item valuations are separable. For this case, we design a mechanism that obtains at least a constant fraction of the optimal welfare, by using a menu of posted prices. This mechanism is also independent of the demand structure, but makes a relatively stronger assumption on the contracts between intermediaries and buyers, namely that each intermediary prefers outcomes with a higher sum of utilities of the subset of buyers represented by it