Filters








39 Hits in 4.2 sec

Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities [article]

Nima Anari, Tung Mai, Shayan Oveis Gharan, Vijay V. Vazirani
2017 arXiv   pre-print
We give constant factor algorithms for a substantial generalization of their problem -- to the case of separable, piecewise-linear concave utility functions.  ...  Recently Cole and Gkatzelis gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash Social  ...  The utility of each agent is separable over item types, but over each item type it is piecewise-linear concave.  ... 
arXiv:1612.05191v3 fatcat:pyan3eku35gw7ireoqu6nbzx6m

Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities [chapter]

Nima Anari, Tung Mai, Shayan Oveis Gharan, Vijay V. Vazirani
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We give constant factor algorithms for a substantial generalization of their problem -to the case of separable, piecewise-linear concave utility functions.  ...  Recently Cole and Gkatzelis [CG15] gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash  ...  For item type i, assume that we have a supply of k i units. The utility of each agent is separable over item types, but over each item type it is piecewise-linear concave.  ... 
doi:10.1137/1.9781611975031.147 dblp:conf/soda/AnariMGV18 fatcat:lngxxaondnh4xm4s43rw4qk7pe

Nash Social Welfare Approximation for Strategic Agents [article]

Simina Brânzei, Vasilis Gkatzelis, Ruta Mehta
2017 arXiv   pre-print
A fundamental objective function used for measuring fair outcomes is the Nash social welfare, defined as the geometric mean of the agent utilities.  ...  In this work we focus on the question of (approximately) implementing the Nash social welfare.  ...  equilibrium of the Fisher market mechanism approximate the optimal Nash social welfare within a factor of 2 for linear valuations.  ... 
arXiv:1607.01569v3 fatcat:66b7bafrirflvjyikrtryq3ifu

Satiation in Fisher Markets and Approximation of Nash Social Welfare [article]

Jugal Garg, Martin Hoefer, Kurt Mehlhorn
2019 arXiv   pre-print
Beyond natural applications in economics, these markets arise in the context of maximizing Nash social welfare when allocating indivisible items to agents.  ...  We show how (approximate) equilibria can be rounded and provide the first constant-factor approximation algorithm (with a factor of 2.404) for maximizing Nash social welfare when agents have budget-additive  ...  Nash social welfare for indivisible items under separable, piecewise-linear concave utilities. In Proc. 29th Symp. Discrete Algorithms (SODA), pages 2274–2290, 2018.  ... 
arXiv:1707.04428v3 fatcat:qqsywhxufvexrkaxz3qzba5gie

Earning Limits in Fisher Markets with Spending-Constraint Utilities [chapter]

Xiaohui Bei, Jugal Garg, Martin Hoefer, Kurt Mehlhorn
2017 Lecture Notes in Computer Science  
Finally, we discuss how our algorithm can be used to obtain in polynomial time a 2-approximation for Nash social welfare in multi-unit markets with indivisible items that come in multiple copies.  ...  Beyond several applications, in which earning limits are natural, equilibria of such markets are a central concept in the allocation of indivisible items to maximize Nash social welfare.  ...  Approximating optimal allocations of indivisible items that maximize Nash social welfare has been studied recently for markets with additive [6, 8] and separable concave valuations [1] .  ... 
doi:10.1007/978-3-319-66700-3_6 fatcat:64kvwik6dfcnlppdpzalfvn54e

The Unreasonable Fairness of Maximum Nash Welfare

Ioannis Caragiannis, David Kurokawa, Hervé Moulin, Ariel D. Procaccia, Nisarg Shah, Junxing Wang
2016 Proceedings of the 2016 ACM Conference on Economics and Computation - EC '16  
The maximum Nash welfare (MNW) solution -which selects an allocation that maximizes the product of utilities -is known to provide outstanding fairness guarantees when allocating divisible goods.  ...  These results lead us to believe that MNW is the ultimate solution for allocating indivisible goods, and underlie its deployment on a popular fair division website.  ...  the optimality of the Nash welfare under A.  ... 
doi:10.1145/2940716.2940726 dblp:conf/sigecom/CaragiannisKMP016 fatcat:urs3ptwnrfdehmc3xfap3rfxcu

Approximating Nash Social Welfare under Rado Valuations [article]

Jugal Garg, Edin Husic, Laszlo A. Vegh
2020 arXiv   pre-print
We consider the problem of approximating maximum Nash social welfare (NSW) while allocating a set of indivisible items to n agents.  ...  We present the first constant-factor approximation algorithm for the symmetric case under Rado valuations.  ...  Nash social welfare problem under Rado valuations.  ... 
arXiv:2009.14793v1 fatcat:ftww5hpifjawpdb2kwkhbkjbm4

Competitive Division of a Mixed Manna

Anna Bogomolnaia, Herve Moulin, Fedor Sandomirskiy, Elena Yanovskaya
2017 Social Science Research Network  
If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale-Eisenberg): hence it is welfarist  ...  Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods.  ...  It is easy to see that v is also 1homogeneous if and only if we can choose β k = 0 for all k. So the simplest utilities in H(A) are additive, v(y) = α · y, and piecewise linear.  ... 
doi:10.2139/ssrn.2914241 fatcat:vifflsuzyrefpjnnccitqndeli

Convex Program Duality, Fisher Markets, and Nash Social Welfare

Richard Cole, Nikhil Devanur, Vasilis Gkatzelis, Kamal Jain, Tung Mai, Vijay V. Vazirani, Sadra Yazdanbod
2017 Proceedings of the 2017 ACM Conference on Economics and Computation - EC '17  
Recently, Cole and Gkatzelis [7] gave the first constant factor approximation algorithm for the problem of maximizing the Nash social welfare (NSW).  ...  We study Fisher markets and the problem of maximizing the Nash social welfare (NSW), and show several closely related new results.  ...  A new program for the Nash social welfare problem In this section we focus on the APX-hard problem of maximizing the NSW with indivisible items [7, 19] .  ... 
doi:10.1145/3033274.3085109 dblp:conf/sigecom/0001DGJMVY17 fatcat:2lpui7itaffvzbjvwsd6jffymi

Competitive Division of a Mixed Manna

Anna Bogomolnaia, Hervé Moulin, Fedor Sandomirskiy, Elena Yanovskaya
2017 Econometrica  
If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale-Eisenberg): hence it is welfarist  ...  Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods.  ...  It is easy to see that v is also 1homogeneous if and only if we can choose β k = 0 for all k. So the simplest utilities in H(A) are additive, v(y) = α · y, and piecewise linear.  ... 
doi:10.3982/ecta14564 fatcat:ohrjsnigqbbipp6sabalexxuky

Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings [article]

Jugal Garg, Pooja Kulkarni, Rucha Kulkarni
2019 arXiv   pre-print
We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations.  ...  Allocations of high valued items are done separately by un-matching certain items and re-matching them, by processes that are different in both algorithms.  ...  We thank Chandra Chekuri and Kent Quanrud for pointing us to relevant literature in submodular function maximization theory, and having several fruitful discussions about the same.  ... 
arXiv:1912.12541v1 fatcat:jmzh6l4eynhdnnje6kcca6wkdi

Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite [article]

Ioannis Panageas, Thorben Tröbst, Vijay V. Vazirani
2021 arXiv   pre-print
Additionally, we define for the first time a Nash-bargaining-based model for non-bipartite matching markets and solve it using CGD.  ...  We give natural applications for each model studied. These models inherit the game-theoretic and computational properties of Nash bargaining.  ...  Acknowledgements The third author would like to profusely thank Federico Echenique for valuable discussions on the principles of mathematical economics.  ... 
arXiv:2106.02024v2 fatcat:rlfq5rztb5aeznch47a2jfshra

Combination Exchange Mechanisms for Efficient Bandwidth Allocation

Rahul Jain, Pravin P. Varaiya
2003 Communications in Information and Systems  
It is well-known that economic efficiency i.e., maximization of social welfare is related to competitive equilibrium [26] .  ...  Next we see a TU network with nonlinear concave utilities for which there is no competitive equilibrium. Example 3. Consider a network with two links, each with two trunks of capacity.  ...  We showed that under the continuum model, the prices the mechanism announces are competitive prices and the allocation is a competitive allocation. Apendix. Proof of theorem 2. Proof.  ... 
doi:10.4310/cis.2003.v3.n4.a5 fatcat:hbe4mfn7wrgojezmrvkab3ocuy

Auction Algorithms for Market Equilibrium with Weak Gross Substitute Demands and their Applications [article]

Jugal Garg, Edin Husić, László A. Végh
2020 arXiv   pre-print
relaxation of the Nash social welfare (NSW) problem.  ...  This leads to a polynomial-time constant factor approximation algorithm for NSW with budget additive separable piecewise linear utility functions; only a pseudopolynomial approximation algorithm was known  ...  Acknowledgment We would like to thank anonymous referees for their comments and suggestions that have helped to improve the presentation of the paper.  ... 
arXiv:1908.07948v3 fatcat:bbb2xvpgyvaddhyuujhql5k3su

Computing Equilibria in Markets with Budget-Additive Utilities [article]

Xiaohui Bei, Jugal Garg, Martin Hoefer, Kurt Mehlhorn
2016 arXiv   pre-print
We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each  ...  They extend the standard case of linear utilities and have been studied in a variety of other market models.  ...  They constitute a special class of separable piecewise-linear concave (SPLC) utilities, where each piecewise-linear component consists of two segments with the second one being constant.  ... 
arXiv:1603.07210v2 fatcat:yfi3nn7izzbutbivcteqdqcj4y
« Previous Showing results 1 — 15 out of 39 results