scholarly journals Finding Fair and Efficient Allocations for Matroid Rank Valuations

2021 ◽  
Vol 9 (4) ◽  
pp. 1-41
Author(s):  
Nawal Benabbou ◽  
Mithun Chakraborty ◽  
Ayumi Igarashi ◽  
Yair Zick
Keyword(s):  
Convex Function ◽  
Real World ◽  
Function Class ◽  
Efficient Allocation ◽  
Indivisible Goods ◽  
Valuation Function ◽  
Bipartite Matching ◽  
Optimal Outcomes ◽  
Efficient Allocations ◽  
Rank Functions

In this article, we present new results on the fair and efficient allocation of indivisible goods to agents whose preferences correspond to matroid rank functions . This is a versatile valuation class with several desirable properties (such as monotonicity and submodularity), which naturally lends itself to a number of real-world domains. We use these properties to our advantage; first, we show that when agent valuations are matroid rank functions, a socially optimal (i.e., utilitarian social welfare-maximizing) allocation that achieves envy-freeness up to one item (EF1) exists and is computationally tractable. We also prove that the Nash welfare-maximizing and the leximin allocations both exhibit this fairness/efficiency combination by showing that they can be achieved by minimizing any symmetric strictly convex function over utilitarian optimal outcomes. To the best of our knowledge, this is the first valuation function class not subsumed by additive valuations for which it has been established that an allocation maximizing Nash welfare is EF1. Moreover, for a subclass of these valuation functions based on maximum (unweighted) bipartite matching, we show that a leximin allocation can be computed in polynomial time. Additionally, we explore possible extensions of our results to fairness criteria other than EF1 as well as to generalizations of the above valuation classes.

scholarly journals Optimal selection policies for a sequence of candidate drugs

2008 ◽  
Vol 40 (02) ◽  
pp. 359-376 ◽  
Author(s):  
C. Charalambous ◽  
J. C. Gittins
Keyword(s):  
Pharmaceutical Companies ◽  
Optimal Selection ◽  
Efficient Allocation ◽  
Allocation Of Resources ◽  
Preclinical Research ◽  
Research Project ◽  
Starting Point ◽  
Optimal Policies ◽  
Efficient Allocations ◽  
Selection Of

Pharmaceutical companies have to face huge risks and enormous costs of production before they can produce a drug. Efficient allocation of resources is essential to help in maximizing profits. Yu and Gittins (2007) described a model and associated software for determining efficient allocations for a preclinical research project. This is the starting point for this paper. We provide explicit optimal policies for the selection of successive candidate drugs for two restricted versions of the Yu and Gittins (2007) model. To some extent these policies are likely to be applicable to the unrestricted model.

scholarly journals Equitable Allocations of Indivisible Goods

2019 ◽  
Author(s):  
Rupert Freeman ◽  
Sujoy Sikdar ◽  
Rohit Vaish ◽  
Lirong Xia
Keyword(s):  
Economic Efficiency ◽  
Pareto Optimality ◽  
Real World ◽  
Fair Division ◽  
Prior Work ◽  
Indivisible Goods ◽  
Preference Data ◽  
Novel Algorithm

In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied (approximate) equitability in isolation, we consider equitability in conjunction with other well-studied notions of fairness and economic efficiency. We show that the Leximin algorithm produces an allocation that satisfies equitability up to any good and Pareto optimality. We also give a novel algorithm that guarantees Pareto optimality and equitability up to one good in pseudopolynomial time.  Our experiments on real-world preference data reveal that approximate envy-freeness, approximate equitability, and Pareto optimality can often be achieved simultaneously.

scholarly journals On the Proximity of Markets with Integral Equilibria

2019 ◽  
Vol 33 ◽  
pp. 1748-1755 ◽  
Author(s):  
Siddharth Barman ◽  
Sanath Kumar Krishnamurthy
Keyword(s):  
Polynomial Time ◽  
Fair Division ◽  
Prior Work ◽  
Indivisible Goods ◽  
Polynomial Time Algorithms ◽  
Fairness And Efficiency ◽  
Pareto Efficient ◽  
Efficient Allocations ◽  
Strong Existence ◽  
Strongly Polynomial

We study Fisher markets that admit equilibria wherein each good is integrally assigned to some agent. While strong existence and computational guarantees are known for equilibria of Fisher markets with additive valuations (Eisenberg and Gale 1959; Orlin 2010), such equilibria, in general, assign goods fractionally to agents. Hence, Fisher markets are not directly applicable in the context of indivisible goods. In this work we show that one can always bypass this hurdle and, up to a bounded change in agents’ budgets, obtain markets that admit an integral equilibrium. We refer to such markets as pure markets and show that, for any given Fisher market (with additive valuations), one can efficiently compute a “near-by,” pure market with an accompanying integral equilibrium.Our work on pure markets leads to novel algorithmic results for fair division of indivisible goods. Prior work in discrete fair division has shown that, under additive valuations, there always exist allocations that simultaneously achieve the seemingly incompatible properties of fairness and efficiency (Caragiannis et al. 2016); here fairness refers to envyfreeness up to one good (EF1) and efficiency corresponds to Pareto efficiency. However, polynomial-time algorithms are not known for finding such allocations. Considering relaxations of proportionality and EF1, respectively, as our notions of fairness, we show that fair and Pareto efficient allocations can be computed in strongly polynomial time.

scholarly journals Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity

2019 ◽  
Vol 33 ◽  
pp. 1877-1884 ◽  
Author(s):  
John P. Dickerson ◽  
Karthik Abinav Sankararaman ◽  
Aravind Srinivasan ◽  
Pan Xu
Keyword(s):  
Real World ◽  
The Other ◽  
Objective Functions ◽  
Bipartite Matching ◽  
Matching Problems ◽  
Special Cases ◽  
Coverage Function ◽  
Synthetic Datasets ◽  
Novel Algorithms ◽  
Real World Problems

In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance—modeled via total weight—of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (OSBM) problem, where the goal is to maximize a submodular function f over the set of matched edges. This objective is general enough to capture the notion of both diversity (e.g., a weighted coverage function) and relevance (e.g., the traditional linear function)—as well as many other natural objective functions occurring in practice (e.g., limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms.

Deterioration of liver function after transarterial chemoembolization (TACE) in hepatocellular carcinoma (HCC): An exploratory analysis of OPTIMIS—An international observational study assessing the use of sorafenib after TACE.

2018 ◽  
Vol 36 (4_suppl) ◽  
pp. 368-368 ◽  
Author(s):  
Masatoshi Kudo ◽  
Jean-Luc Raoul ◽  
Han Chu Lee ◽  
Ann-Lii Cheng ◽  
Keiko Nakajima ◽  
...  
Keyword(s):  
Liver Function ◽  
Real World ◽  
International Normalized Ratio ◽  
Exploratory Analysis ◽  
The Real ◽  
Optimal Outcomes ◽  
Real World Setting ◽  
Selection For ◽  
B 52 ◽  
Clinical Trial Information

368 Background: TACE is commonly used for patients (pts) with unresectable HCC, and appropriate pt selection is important to obtain optimal outcomes. However, there is no globally accepted consensus on unsuitability and refractoriness to TACE. Retrospective studies suggest that continuing TACE after refractoriness or failure is harmful and may cause pts to become ineligible for further treatments because of liver function deterioration. This exploratory analysis of OPTIMIS evaluated the real-world incidence of liver function deterioration by baseline liver characteristics after first TACE. Methods: OPTIMIS enrolled 1670 pts with HCC for whom a decision to treat with TACE was made at the time of study entry. Liver function deterioration was defined as worsening of CTCAE grade compared with baseline for any of these parameters: aspartate aminotransferase (AST), alanine aminotransferase (ALT), total bilirubin, albumin, and prothrombin international normalized ratio (INR). All analyses are descriptive. Results: A total of 977 pts received TACE. The incidence of liver deterioration was higher in pts with BCLC stage C vs stage B (52% vs 44%, respectively), in pts exceeding the up-to-7 criteria compared with those within (49% vs 43%, respectively), and in those deemed unsuitable for TACE at baseline versus those deemed eligible (53% vs 44%, respectively) (Table). Conclusions: Deterioration of liver function parameters was observed after TACE in pts with HCC in the real-world setting. Therefore, appropriate pt selection for TACE and preserving liver function are important to optimize the benefit of TACE and subsequent treatments. Clinical trial information: NCT01933945. [Table: see text]

scholarly journals Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints

2019 ◽  
Vol 33 ◽  
pp. 2045-2052 ◽  
Author(s):  
Ayumi Igarashi ◽  
Dominik Peters
Keyword(s):  
Maximum Degree ◽  
Optimal Allocation ◽  
Additional Constraint ◽  
Pareto Optimal ◽  
Np Hard ◽  
Efficient Allocation ◽  
Indivisible Goods ◽  
Underlying Graph

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity of fair allocations. We study the problem of finding an allocation that is Pareto-optimal. While it is easy to find an efficient allocation when the underlying graph is a path or a star, the problem is NP-hard for many other graph topologies, even for trees of bounded pathwidth or of maximum degree 3. We show that on a path, there are instances where no Pareto-optimal allocation satisfies envy-freeness up to one good, and that it is NP-hard to decide whether such an allocation exists, even for binary valuations. We also show that, for a path, it is NP-hard to find a Pareto-optimal allocation that satisfies maximin share, but show that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.

scholarly journals Fair Allocation of Indivisible Goods to Asymmetric Agents

2019 ◽  
Vol 64 ◽  
pp. 1-20 ◽  
Author(s):  
Alireza Farhadi ◽  
Mohammad Ghodsi ◽  
Mohammad Taghi Hajiaghayi ◽  
Sébastien Lahaie ◽  
David Pennock ◽  
...  
Keyword(s):  
Real World ◽  
Simple Algorithm ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Real World Data ◽  
The Subject ◽  
Approximation Guarantee ◽  
To Receive ◽  
Positive Results ◽  
Better Than

We study fair allocation of indivisible goods to agents with unequal entitlements. Fair allocation has been the subject of many studies in both divisible and indivisible settings. Our emphasis is on the case where the goods are indivisible and agents have unequal entitlements. This problem is a generalization of the work by Procaccia and Wang (2014) wherein the agents are assumed to be symmetric with respect to their entitlements. Although Procaccia and Wang show an almost fair (constant approximation) allocation exists in their setting, our main result is in sharp contrast to their observation. We show that, in some cases with n agents, no allocation can guarantee better than 1/n approximation of a fair allocation when the entitlements are not necessarily equal. Furthermore, we devise a simple algorithm that ensures a 1/n approximation guarantee. Our second result is for a restricted version of the problem where the valuation of every agent for each good is bounded by the total value he wishes to receive in a fair allocation. Although this assumption might seem without loss of generality, we show it enables us to find a 1/2 approximation fair allocation via a greedy algorithm. Finally, we run some experiments on real-world data and show that, in practice, a fair allocation is likely to exist. We also support our experiments by showing positive results for two stochastic variants of the problem, namely stochastic agents and stochastic items.

scholarly journals Efficiency and endogenous fertility

2019 ◽  
Vol 14 (2) ◽  
pp. 475-512 ◽  
Author(s):  
Mikel Pérez-Nievas ◽  
José I. Conde-Ruiz ◽  
Eduardo L. Giménez
Keyword(s):  
Birth Order ◽  
Low Income ◽  
Positive Measure ◽  
Overlapping Generations ◽  
Finite Horizon ◽  
Value Functions ◽  
Efficient Allocation ◽  
Endogenous Fertility ◽  
Efficient Allocations ◽  
Fertility Choices

This paper explores the properties of the notions of A ‐efficiency and P ‐efficiency, which were proposed by Golosov et al.. (2007), to evaluate allocations in a general overlapping generations setting in which fertility choices are endogenously selected from a continuum and any two agents of the same generation are identical. First, we show that the properties of A ‐efficient allocations vary depending on the criterion used to identify potential agents. If one identifies potential agents by their position in their siblings' birth order, as Golosov, Jones, and Tertilt do, then A ‐efficiency requires that a positive measure of agents use most of their endowment to maximize the utility of the dynasty head, which, in environments with finite‐horizon altruism, implies that some agents—the youngest in every family—obtain an arbitrary low income to finance their own consumption and fertility plans. If potential agents are identified by the dates in which they may be born, then A ‐efficiency reduces to dynastic maximization, which, in environments with finite‐horizon altruism, drives the economy to a collapse in finite time. To deal with situations like those arising in economies with finite‐horizon altruism, in which A ‐efficiency may be in conflict with individual rights, we propose to evaluate the efficiency of a given allocation with a particular class of specifications of P ‐efficiency for which the utility attributed to the unborn depends on the utility obtained by their living siblings. Under certain concavity assumptions on value functions, we also characterize every symmetric, P ‐efficient allocation as a Millian efficient allocation, that is, as a symmetric allocation that is not A ‐dominated—with the birth‐order criterion—by any other symmetric allocation.

Interprofessional and Interdisciplinary Learning

2010 ◽  
pp. 1-13 ◽  
Author(s):  
Steve Smith ◽  
Lynn Clouder
Keyword(s):  
Real World ◽  
Boundary Crossing ◽  
Multiple Perspectives ◽  
Interdisciplinary Learning ◽  
The Real ◽  
Optimal Outcomes ◽  
Collaborative Education

This chapter begins by considering the words used to discuss collaborative education. Although it can be argued that “practice” separates “a profession” from “a discipline”, the merit in separating theory from practice is highly questionable. The literature suggests that the challenges to interprofessional and interdisciplinary learning are very similar, for example, the “silo” mentality causes problems within both. In addition, it is evident that the reasons behind advocacy of interprofessional and interdisciplinary learning are also similar. The chapter demonstrates that successful interprofessional and interdisciplinary learning requires fundamental changes to both the curriculum and the organisation delivering it. The authors conclude that while subtle differences might exist between interprofessional and interdisciplinary learning their promotion is based on a similar rationale, which is to ensure that students are prepared for the real world in which collaboration, boundary crossing, adopting multiple perspectives and working with others to achieve optimal outcomes, is paramount.

scholarly journals Competition May Increase Social Utility in Bipartite Matching Problem

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yi-Xiu Kong ◽  
Guang-Hui Yuan ◽  
Lei Zhou ◽  
Rui-Jie Wu ◽  
Gui-Yuan Shi
Keyword(s):  
Real World ◽  
Social Utility ◽  
Preference Structure ◽  
Matching Problem ◽  
Social Phenomena ◽  
Bipartite Matching ◽  
Men And Women

Bipartite matching problem is to study two disjoint groups of agents who need to be matched pairwise. It can be applied to many real-world scenarios and explain many social phenomena. In this article, we study the effect of competition on bipartite matching problem by introducing conformity into the preference structure. The results show that a certain amount of competition can improve the overall utility of society and also eliminate the giant shift of social utility when matching unequal numbers of men and women.

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