Auctions with Heterogeneous Items and Budget Limits

We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations

Envy, Regret, and Social Welfare Loss

Incentive compatibility (IC) is a desirable property for any auction mechanism, including those used in online advertising. However, in real world applications practical constraints and complex environments often result in mechanisms that lack incentive compatibility. Recently, several papers investigated the problem of deploying black-box statistical tests to determine if an auction mechanism is incentive compatible by using the notion of IC-Regret that measures the regret of a truthful bidder. Unfortunately, most of those methods are computationally intensive, since they require the execution of many counterfactual experiments. In this work, we show that similar results can be obtained using the notion of IC-Envy. The advantage of IC-Envy is its efficiency: it can be computed using only the auction's outcome. In particular, we focus on position auctions. For position auctions, we show that for a large class of pricing schemes (which includes e.g. VCG and GSP), IC-Envy ≥ IC-Regret (and IC-Envy = IC-Regret under mild supplementary conditions). Our theoretical results are completed showing that, in the position auction environment, IC-Envy can be used to bound the loss in social welfare due to the advertiser untruthful behavior. Finally, we show experimentally that IC-Envy can be used as a feature to predict IC-Regret in settings not covered by the theoretical results. In particular, using IC-Envy yields better results than training models using only price and value features

Controlled-release oxycodone and pregabalin in the treatment of neuropathic pain: results of a multicenter Italian study

Abstract AIMS: The aim of our study was to compare the efficacy, safety, and quality of life of combination therapy with controlled-release (CR) oxycodone plus pregabalin versus monotherapy with either CR oxycodone or pregabalin in patients with neuropathic pain. MATERIALS AND METHODS: Patients with moderate to severe neuropathic pain, despite the use of various pharmacologic treatments prior to study entry, were enrolled (n = 409) and treated with CR oxycodone plus pregabalin (n = 169), CR oxycodone (n = 106), and pregabalin (n = 134). Pain intensity was rated on an 11-point numerical rating scale (NRS). RESULTS: The combination of CR oxycodone plus pregabalin and CR oxycodone monotherapy were both more effective for alleviating neuropathic pain than pregabalin monotherapy (reduction in NRS value: 80, 76, and 46%, respectively; p </= 0.003). Significantly greater improvements from baseline in quality of life were reported with combination therapy than with monotherapy (p = 0.0009). At the end of treatment, the majority (91.2%) of patients receiving CR oxycodone plus pregabalin found that the treatment had been 'effective' or 'very effective'. Combination therapy also allowed a dose reduction of both agents (22% for CR oxycodone and 51% for pregabalin) compared with the dosages of the respective monotherapies. Combination therapy had a superior safety profile compared with pregabalin monotherapy. CONCLUSIONS: The combination of CR oxycodone plus pregabalin may represent a valuable addition to the existing pharmacotherapy for neuropathic pain and warrants further investigation

Efficiency Guarantees in Auctions with Budgets

In settings where players have a limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor then the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one incentive-compatible auction that always outputs a Pareto-efficient solution, or that no truthful mechanism can always guarantee a Pareto-efficient outcome. Traditionally, impossibility results can be avoided by considering approximations. However, Pareto-efficiency is a binary property (is either satisfied or not), which does not allow for approximations. In this paper we propose a new notion of efficiency, called \emph{liquid welfare}. This is the maximum amount of revenue an omniscient seller would be able to extract from a certain instance. We explain the intuition behind this objective function and show that it can be 2-approximated by two different auctions. Moreover, we show that no truthful algorithm can guarantee an approximation factor better than 4/3 with respect to the liquid welfare, and provide a truthful auction that attains this bound in a special case. Importantly, the liquid welfare benchmark also overcomes impossibilities for some settings. While it is impossible to design Pareto-efficient auctions for multi-unit auctions where players have decreasing marginal values, we give a deterministic $O(\log n)$-approximation for the liquid welfare in this setting

Gerir a diversidade: contributos da aprendizagem cooperativa para a construção de salas de aula inclusivas

The action-research we have held at the primary education, in a school placed near the town of Tomar, in 2009-2010, under the master's degree in Special Education, was the starting point for writing this article. The research had as main objective to promote the successful learning of a heterogeneous group of students, where a child considered with longstanding special educational needs is included – diagnosis of galactosaemia and cognitive impairment. Starting from the educational context of a particular classroom of 2nd and 3rd grades, where we were working as special education teacher, we had created an inclusive learning environment for each student in the class. Through effective collaboration between fellow teachers, we generated changes in methodologies, breaking with some traditional practices in the classroom, when regular teachers and special education are in the same learning space. By a systematic implementation of cooperative learning strategies among students, and applying qualitative data gathering techniques of research, before and after the intervention – interview, naturalistic observation, sociometry and documental research –, we have increased the quality and quantity of learning and promoted another way of ‘looking to’ the difference

The asymptotic price of anarchy for k-uniform congestion games

We consider the atomic version of congestion games with affine cost functions, and analyze the quality of worst case Nash equilibria when the strategy spaces of the players are the set of bases of a k-uniform matroid. In this setting, for some parameter k, each player is to choose k out of a finite set of resources, and the cost of a player for choosing a resource depends affine linearly on the number of players choosing the same resource. Earlier work shows that the price of anarchy for this class of games is larger than 1.34 but at most 2.15. We determine a tight bound on the asymptotic price of anarchy equal to ≈1.35188. Here, asymptotic refers to the fact that the bound holds for all instances with sufficiently many players. In particular, the asymptotic price of anarchy is bounded away from 4/3. Our analysis also yields an upper bound on the price of anarchy <1.4131, for all instances

Controlled-release oxycodone and pregabalin in the treatment of neuropathic pain: results of a multicenter Italian study

Aims: The aim of our study was to compare the efficacy, safety, and quality of life of combination therapy with controlled-release (CR) oxycodone plus pregabalin versus monotherapy with either CR oxycodone or pregabalin in patients with neuropathic pain. Materials and Methods: Patients with moderate to severe neuropathic pain, despite the use of various pharmacologic treatments prior to study entry, were enrolled (n = 409) and treated with CR oxycodone plus pregabalin (n = 169), CR oxycodone (n = 106), and pregabalin (n = 134). Pain intensity was rated on an 11-point numerical rating scale (NRS). Results: The combination of CR oxycodone plus pregabalin and CR oxycodone monotherapy were both more effective for alleviating neuropathic pain than pregabalin monotherapy ( reduction in NRS value: 80, 76, and 46%, respectively; p <= 0.003). Significantly greater improvements from baseline in quality of life were reported with combination therapy than with monotherapy ( p = 0.0009). At the end of treatment, the majority (91.2%) of patients receiving CR oxycodone plus pregabalin found that the treatment had been 'effective' or 'very effective'. Combination therapy also allowed a dose reduction of both agents (22% for CR oxycodone and 51% for pregabalin) compared with the dosages of the respective monotherapies. Combination therapy had a superior safety profile compared with pregabalin monotherapy. Conclusions: The combination of CR oxycodone plus pregabalin may represent a valuable addition to the existing pharmacotherapy for neuropathic pain and warrants further investigation. Copyright (c) 2008 S. Karger AG, Base

Stochastic bandits for multi-platform budget optimization in online advertising

We study the problem of an online advertising system that wants to optimally spend an advertiser's given budget for a campaign across multiple platforms, without knowing the value for showing an ad to the users on those platforms. We model this challenging practical application as a Stochastic Bandits with Knapsacks problem over T rounds of bidding with the set of arms given by the set of distinct bidding m-tuples, where m is the number of platforms. We modify the algorithm proposed in Badanidiyuru et al., [11] to extend it to the case of multiple platforms to obtain an algorithm for both the discrete and continuous bid-spaces. Namely, for discrete bid spaces we give an algorithm with regret , where OPT is the performance of the optimal algorithm that knows the distributions. For continuous bid spaces the regret of our algorithm is . When restricted to this special-case, this bound improves over Sankararaman and Slivkins [34] in the regime OPT &lt; &lt; T, as is the case in the particular application at hand. Second, we show an lower bound for the discrete case and an ?(m1/3B2/3) lower bound for the continuous setting, almost matching the upper bounds. Finally, we use a real-world data set from a large internet online advertising company with multiple ad platforms and show that our algorithms outperform common benchmarks and satisfy the required properties warranted in the real-world application

Approximately efficient two-sided combinatorial auctions

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible. Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers' valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain "unnatural" transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms

Approximately efficient two-sided combinatorial auctions

We develop and extend a line of recent work on the design of mechanisms for two-sided markets. The markets we consider consist of buyers and sellers of a number of items, and the aim of a mechanism is to improve the social welfare by arranging purchases and sales of the items. A mechanism is given prior distributions on the agents' valuations of the items, but not the actual valuations; thus, the aim is to maximise the expected social welfare over these distributions. As in previous work, we are interested in the worst-case ratio between the social welfare achieved by a truthful mechanism and the best social welfare possible. Our main result is an incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers' valuations are additive. This is the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions. To achieve this result, we introduce a more general kind of demand query that seems to be needed in this situation. In the simpler case that sellers have unit supply (each having just one item to sell), we give a new mechanism whose welfare guarantee improves on a recent one in the literature. We also introduce a more demanding version of the strong budget balance (SBB) criterion, aimed at ruling out certain "unnatural" transactions satisfied by SBB. We show that the stronger version is satisfied by our mechanisms