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

Ioannis Panageas, Thorben Tröbst, Vijay V. Vazirani
2022 arXiv   pre-print
This led [Hosseini and Vazirani 2021] to define a rich collection of Nash-bargaining-based models for one-sided and two-sided matching markets, in both Fisher and Arrow-Debreu settings, together with implementations  ...  We rectify this to the extent possible by showing that these models satisfy approximate equal-share fairness notions. 3) We define, for the first time, a model for non-bipartite matching markets under  ...  Our Nash-bargaining-based model for non-bipartite matching markets, given in Section 3, is the first of its kind. 3).  ... 
arXiv:2106.02024v3 fatcat:k3dd3dsoingwvnzri7vun3od3e

Nash-Bargaining-Based Models for Matching Markets: One-Sided and Two-Sided; Fisher and Arrow-Debreu [article]

Mojtaba Hosseini, Vijay V. Vazirani
2021 arXiv   pre-print
We also give very fast implementations for these models which solve large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.  ...  Our approach yields a rich collection of models: for one-sided as well as two-sided markets, for Fisher as well as Arrow-Debreu settings, and for a wide range of utility functions, all the way from linear  ...  They also defined and developed algorithms for the non-bipartite matching market model. Lastly, they gave the connection between HZ and the Nash-bargaining-based models stated above.  ... 
arXiv:2105.10704v3 fatcat:loomnwk3tvbovctfiy6fckx7ea

The cooperative game theory foundations of network bargaining games [article]

MohammadHossein Bateni and MohammadTaghi Hajiaghayi and Nicole Immorlica and Hamid Mahini
2010 arXiv   pre-print
We simplify and generalize these results to a setting in which participants in only one side of the market are limited to one contract each.  ...  of stable and balanced defined for the bargaining games.  ...  The authors would like to acknowledge Éva Tardos for suggesting possible connections with the cooperative game theory literature.  ... 
arXiv:1004.4317v1 fatcat:xbjojgwfbveehf5tbwsr764k2q

The Cooperative Game Theory Foundations of Network Bargaining Games [chapter]

MohammadHossein Bateni, MohammadTaghi Hajiaghayi, Nicole Immorlica, Hamid Mahini
2010 Lecture Notes in Computer Science  
We simplify and generalize these results to a setting in which participants in only one side of the market are limited to one contract each.  ...  for the bargaining games.  ...  The authors would like to acknowledge Eva Tardos for suggesting possible connections with the cooperative game theory literature.  ... 
doi:10.1007/978-3-642-14165-2_7 fatcat:vgqho6gtk5bphcxjmjaphnjvda

Rational Convex Programs, Their Feasibility, and the Arrow-Debreu Nash Bargaining Game [article]

Vijay V. Vazirani
2010 arXiv   pre-print
We give an application of our combinatorial algorithm for ADNB to an important "fair" throughput allocation problem on a wireless channel.  ...  The specific problem we study pertains to a Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model.  ...  We illustrate this by comparing the algorithms for the problems of maximum weight perfect matching and maximum weight matching in bipartite graphs in Section 10.  ... 
arXiv:1010.4280v1 fatcat:blogv4lhjrg6poyp4ilidxlxfq

The notion of a rational convex program, and an algorithm for the arrow-debreu Nash bargaining game

Vijay V. Vazirani
2012 Journal of the ACM  
Next we define a new Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model.  ...  We give an application of our combinatorial algorithm for ADNB to an important "fair" throughput allocation problem on a wireless channel.  ...  As an example, recall algorithms for finding a maximum weight perfect matching (a non-total problem) and a maximum weight matching (a total problem) in a bipartite graph.  ... 
doi:10.1145/2160158.2160160 fatcat:ymvyez7cqnd3zhh3oy22mooxim

The Notion of a Rational Convex Program, and an Algorithm for the Arrow-Debreu Nash Bargaining Game [chapter]

Vijay V. Vazirani
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
Next we define a new Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model.  ...  We give an application of our combinatorial algorithm for ADNB to an important "fair" throughput allocation problem on a wireless channel.  ...  As an example, recall algorithms for finding a maximum weight perfect matching (a non-total problem) and a maximum weight matching (a total problem) in a bipartite graph.  ... 
doi:10.1137/1.9781611973099.78 dblp:conf/soda/Vazirani12 fatcat:yioctv4rgbcpllc4dsflagfrrm

One-Sided Matching Markets with Endowments: Equilibria and Algorithms [article]

Jugal Garg, Thorben Tröbst, Vijay V. Vazirani
2021 arXiv   pre-print
For the dichotomous-utilities case of their model linear Arrow-Debreu Nash bargaining one-sided matching market (1LAD), we give a combinatorial, strongly polynomial-time algorithm and show that it admits  ...  of) Nash-bargaining-based matching market models.  ...  To deal with this reality, [24] defined a rich collection of Nash-bargaining-based matching market models, both one-sided and two-sided, in both Fisher and Arrow-Debreu settings, together with implementations  ... 
arXiv:2009.10320v3 fatcat:kqszsahf55cgjo6c4s4chyutjq

Electronic Markets and Auctions (Dagstuhl Seminar 13461)

Yishay Mansour, Benny Moldovanu, Noam Nisan, Berthold Vöcking, Marc Herbstritt
2014 Dagstuhl Reports  
on algorithmic aspects of mechanism design.  ...  From the computer science perspective, with the advent of the Internet, there has been a significant amount of work in Algorithmic Game Theory focusing on computational aspects of electronic markets and  ...  In particular, we consider two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders.  ... 
doi:10.4230/dagrep.3.11.58 dblp:journals/dagstuhl-reports/MansourMNV13 fatcat:yvkfyeeezrhhnhckygpqseqwx4

Balanced outcomes in social exchange networks

Jon Kleinberg, Éva Tardos
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
Our result exploits connections to the structure of matchings in graphs, including decomposition theorems for graphs with perfect matchings, and also involves the development of new techniques.  ...  Here we resolve these questions, characterizing the possible values of this bargaining solution, and giving an efficient algorithm to compute the set of possible values.  ...  We thank Larry Blume, David Easley, and Ankur Moitra for many discussions and insights, and Michael Macy, Arnout van de Rijt, and Shane Thye for discussions on the sociological context.  ... 
doi:10.1145/1374376.1376994 dblp:conf/stoc/KleinbergT08 fatcat:xqvia4wr7bcpbidouinzkxipfu

Nash-Bargaining-Based Models for Matching Markets: One-Sided and Two-Sided; Fisher and Arrow-Debreu

Mojtaba Hosseini, Vijay V. Vazirani, Mark Braverman
2022
We also give very fast implementations for these models which solve large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.  ...  Our approach yields a rich collection of models: for one-sided as well as two-sided markets, for Fisher as well as Arrow-Debreu settings, and for a wide range of utility functions, all the way from linear  ...  one-sided matching market models based on our Nash bargaining approach.  ... 
doi:10.4230/lipics.itcs.2022.86 fatcat:bixm6yk3m5hjpjb7i72ffwesfu

Approximating the Nash Social Welfare with Indivisible Items

Richard Cole, Vasilis Gkatzelis
2018 SIAM journal on computing (Print)  
., the Nash social welfare. This problem is known to be NP-hard, and our main result is the first efficient constant-factor approximation algorithm for this objective.  ...  , and forcing the agents to spend on lower priced items.  ...  Acknowledgments The second author would like to thank Paul Dütting, Zhiyi Huang, and Tim Roughgarden for stimulating discussions.  ... 
doi:10.1137/15m1053682 fatcat:7vvugmroz5arbhcwoh6ruwpw7m

Approximating the nash social welfare with indivisible items

Richard Cole, Vasilis Gkatzelis
2015 ACM SIGecom Exchanges  
., the Nash social welfare. This problem is known to be NP-hard, and our main result is the first efficient constant-factor approximation algorithm for this objective.  ...  , and forcing the agents to spend on lower priced items.  ...  Acknowledgments The second author would like to thank Paul Dütting, Zhiyi Huang, and Tim Roughgarden for stimulating discussions.  ... 
doi:10.1145/2845926.2845931 fatcat:ueph54uftffxzakb3ftn6npqeu

Nash Bargaining Via Flexible Budget Markets [chapter]

Vijay V. Vazirani
Lecture Notes in Computer Science  
We give an application of our combinatorial algorithm for ADNB to an important "fair" throughput allocation problem on a wireless channel.  ...  The specific problem we study pertains to a Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model.  ...  We illustrate this by comparing the algorithms for the problems of maximum weight perfect matching and maximum weight matching in bipartite graphs in Section 11.  ... 
doi:10.1007/978-3-540-69903-3_2 fatcat:dfduy5g5wnfilc7h6kbqybyfji

Nash Bargaining Via Flexible Budget Markets [chapter]

Vijay V. Vazirani
Lecture Notes in Computer Science  
We give an application of our combinatorial algorithm for ADNB to an important "fair" throughput allocation problem on a wireless channel.  ...  The specific problem we study pertains to a Nash bargaining game, called ADNB, which is derived from the linear case of the Arrow-Debreu market model.  ...  We illustrate this by comparing the algorithms for the problems of maximum weight perfect matching and maximum weight matching in bipartite graphs in Section 11.  ... 
doi:10.1007/978-3-540-68880-8_2 fatcat:hi5fjydczjfcznqo2b6ed3qi6y
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