{"type":"ScholarlyArticle","title":"Exploring Leximin Principle for Fair Core-Selecting Combinatorial Auctions: Payment Rule Design and Implementation","authors":[{"name":"Hao Cheng","slug":"hao-cheng","given":"Hao","family":"Cheng","affiliation":"State Key Laboratory for Novel Software Technology , Nanjing University , China; Nanyang Technological University."},{"name":"Shufeng Kong","slug":"shufeng-kong","given":"Shufeng","family":"Kong","affiliation":"School of Software Engineering , Sun Yat-Sen University , China"},{"name":"Yanchen Deng","slug":"yanchen-deng","given":"Yanchen","family":"Deng","affiliation":"School of Computer Science and Engineering , Nanyang Technological University , Singapore"},{"name":"Caihua Liu","slug":"caihua-liu","given":"Caihua","family":"Liu","affiliation":"School of Artificial Intelligence , Guilin University of Electronic Technology , China"},{"name":"Xiaohu Wu","slug":"xiaohu-wu","given":"Xiaohu","family":"Wu","affiliation":"National Engineering Research Center of Mobile Network Technologies , Beijing University of Posts and Telecommunications , China"},{"name":"Bo An","slug":"bo-an","given":"Bo","family":"An","affiliation":"School of Computer Science and Engineering , Nanyang Technological University , Singapore"},{"name":"Chongjun Wang","slug":"chongjun-wang","given":"Chongjun","family":"Wang","affiliation":"State Key Laboratory for Novel Software Technology , Nanjing University , China"}],"abstract":"Core-selecting combinatorial auctions (CAs) restrict the auction result in the core such that no coalitions could improve their utilities by engaging in collusion. The minimum-revenue-core (MRC) rule is a widely used core-selecting payment rule to maximize the total utilities of all bidders. However, the MRC rule can suffer from severe unfairness since it ignores individuals' utilities. To address this limitation, we propose to explore the leximin principle to achieve fairness in core-selecting CAs since the leximin principle prefers to maximize the utility of the worst-off; the resulting bidder-leximin-optimal (BLO) payment rule is then theoretically analyzed and an effective algorithm is further provided to compute the BLO outcome. Moreover, we conduct extensive experiments to show that our algorithm returns fairer utility distributions and is faster than existing algorithms of core-selecting payment rules.","doi":"10.24963/ijcai.2023/287","url":"https://ijcai.org/proceedings/2023/287","pdf":"https://ijcai.org/proceedings/2023/0287.pdf","markdown":"https://ijcai.org/proceedings/2023/287.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/287","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":287,"pages":{"first":2581,"last":2588},"keywords":["Game Theory and Economic Paradigms: GTEP: Auctions and market-based systems","Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Mechanism design"],"videos":[],"references":[{"position":1,"raw":"[Arin and Inarra, 2001] Javier Arin and Elena Inarra. Egali- tarian solutions in the core. International Journal of Game Theory, 30(2):187-193, 2001.","title":"Javier Arin and Elena Inarra. Egalitarian solutions in the core","authors":"Inarra Arin","year":"2001","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Ausubel and Baranov, 2017] Lawrence M. Ausubel and Oleg Baranov. A practical guide to the combinatorial clock auction. The Economic Journal, 127(605):334-350, 2017.","title":"A practical guide to the combinatorial clock auction","authors":"Lawrence M Ausubel, Oleg Baranov","year":"2017","venue":"The Economic Journal","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Ausubel et al., 2006] Lawrence M Ausubel, Paul Milgrom, et al. The lovely but lonely vickrey auction. Combinatorial Auctions, 17:22-26, 2006.","title":"The lovely but lonely vickrey auction","authors":"Paul Lawrence M Ausubel, Milgrom","year":"2006","venue":"Combinatorial Auctions","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bünz et al., 2015] Benedikt Bünz, Sven Seuken, and Ben- jamin Lubin. A faster core constraint generation algo- rithm for combinatorial auctions. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 827- 834, 2015.","title":"A faster core constraint generation algorithm for combinatorial auctions","authors":"Benedikt Bünz, Sven Seuken, Benjamin Lubin","year":"2015","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Bünz et al., 2018] Benedikt Bünz, Benjamin Lubin, and Sven Seuken. Designing core-selecting payment rules: A computational search approach. In Proceedings of the 2018 ACM Conference on Economics and Computation, pages 109-109, 2018.","title":"Designing core-selecting payment rules: A computational search approach","authors":"Benedikt Bünz, Benjamin Lubin, Sven Seuken","year":"2018","venue":"Proceedings of the 2018 ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Clarke, 1971] Edward H Clarke. Multipart pricing of public goods. Public Choice, pages 17-33, 1971.","title":"Multipart pricing of public goods","authors":"Clarke Edward","year":"1971","venue":"Public Choice","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cramton, 2013] Peter Cramton. Spectrum auction design. Review of Industrial Organization, 42(2):161-190, 2013.","title":"Spectrum auction design","authors":"Peter Cramton","year":"2013","venue":"Review of Industrial Organization","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Day and Cramton, 2012] Robert W Day and Peter Cramton. Quadratic core-selecting payment rules for combinatorial auctions. Operations Research, 60(3):588-603, 2012.","title":"Quadratic core-selecting payment rules for combinatorial auctions","authors":"W Robert, Peter Day, Cramton","year":"2012","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Day and Milgrom, 2008] Robert Day and Paul Milgrom. Core-selecting package auctions. International Journal of Game Theory, 36(3):393-407, 2008.","title":"Robert Day and Paul Milgrom. Core-selecting package auctions","authors":"Milgrom Day","year":"2008","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Day and Raghavan, 2007] Robert W Day and Subramanian Raghavan. Fair payments for efficient allocations in pub- lic sector combinatorial auctions. Management Science, 53(9):1389-1406, 2007.","title":"Fair payments for efficient allocations in public sector combinatorial auctions","authors":"W Robert, Subramanian Day, Raghavan","year":"2007","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Erdil and Klemperer, 2010] Aytek Erdil and Paul Klem- perer. A new payment rule for core-selecting package auc- tions. Journal of the European Economic Association, 8(2- 3):537-547, 2010.","title":"Aytek Erdil and Paul Klemperer. A new payment rule for core-selecting package auc-tions","authors":"Klemperer Erdil","year":"2010","venue":"Journal of the European Economic Association","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gillies, 1959] Donald B Gillies. Solutions to general non- zero-sum games. Contributions to the Theory of Games, 4:47-85, 1959.","title":"Solutions to general nonzero-sum games","authors":"B Donald, Gillies","year":"1959","venue":"Contributions to the Theory of Games","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Goel et al., 2015] Gagan Goel, Mohammad Reza Khani, and Renato Paes Leme. Core-competitive auctions. In Pro- ceedings of the Sixteenth ACM Conference on Economics and Computation, pages 149-166, 2015.","title":"Core-competitive auctions","authors":"Gagan Goel, Mohammad, Reza Khani, Renato Paes, Leme","year":"2015","venue":"Proceedings of the Sixteenth ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Goeree and Lien, 2016] Jacob K Goeree and Yuanchuan Lien. On the impossibility of core-selecting auctions. The- oretical Economics, 11(1):41-52, 2016.","title":"On the impossibility of core-selecting auctions","authors":"K Jacob, Yuanchuan Goeree, Lien","year":"2016","venue":"Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Grötschel et al., 1981] Martin Grötschel, László Lovász, and Alexander Schrijver. The ellipsoid method and its con- sequences in combinatorial optimization. Combinatorica, 1(2):169-197, 1981.","title":"The ellipsoid method and its consequences in combinatorial optimization","authors":"Martin Grötschel, László Lovász, Alexander Schrijver","year":"1981","venue":"Combinatorica","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Groves, 1973] Theodore Groves. Incentives in teams. Econometrica: Journal of the Econometric Society, pages 617-631, 1973.","title":"Theodore Groves. Incentives in teams","authors":"Groves","year":"1973","venue":"Econometrica: Journal of the Econometric Society","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Leyton-Brown et al., 2000] Kevin Leyton-Brown, Mark Pearson, and Yoav Shoham. Towards a universal test suite for combinatorial auction algorithms. In Proceedings of the 2nd ACM Conference on Electronic Commerce, pages 66-76, 2000.","title":"Towards a universal test suite for combinatorial auction algorithms","authors":"Kevin Leyton-Brown, Mark Pearson, Yoav Shoham","year":"2000","venue":"Proceedings of the 2nd ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Leyton-Brown et al., 2017] Kevin Leyton-Brown, Paul Mil- grom, and Ilya Segal. Economics and computer science of a radio spectrum reallocation. Proceedings of the National Academy of Sciences, 114(28):7202-7209, 2017.","title":"Economics and computer science of a radio spectrum reallocation","authors":"Kevin Leyton-Brown, Paul Milgrom, Ilya Segal","year":"2017","venue":"Proceedings of the National Academy of Sciences","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lubin et al., 2015] Benjamin Lubin, Benedikt Bünz, and Sven Seuken. New core-selecting payment rules with bet- ter fairness and incentive properties. In The Third Confer- ence on Auctions, Market Mechanisms and Their Applica- tions. ACM, 2015.","title":"New core-selecting payment rules with better fairness and incentive properties","authors":"Benjamin Lubin, Benedikt Bünz, Sven Seuken","year":"2015","venue":"The Third Conference on Auctions, Market Mechanisms and Their Applications","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Manual, 1987] CPLEX User's Manual. Ibm ilog cplex op- timization studio. Version, 12(1987-2018):1, 1987.","title":"CPLEX User's Manual. Ibm ilog cplex optimization studio","authors":"Manual","year":"1987","venue":"Version","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Niazadeh et al., 2022] Rad Niazadeh, Jason Hartline, Nicole Immorlica, Mohammad Reza Khani, and Brendan Lucier. Fast core pricing for rich advertising auctions. Operations Research, 70(1):223-240, 2022.","title":"Fast core pricing for rich advertising auctions","authors":"Niazadeh","year":"2022","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Rawls, 2004] John Rawls. A theory of justice. In Ethics, pages 229-234. Routledge, 2004.","title":"A theory of justice","authors":"John Rawls","year":"2004","venue":"Ethics","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Rothkopf et al., 1998] Michael H Rothkopf, Aleksandar Pekeč, and Ronald M Harstad. Computationally man- ageable combinational auctions. Management science, 44(8):1131-1147, 1998.","title":"Computationally manageable combinational auctions","authors":"Aleksandar Michael H Rothkopf, Ronald M Pekeč, Harstad","year":"1998","venue":"Management science","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Sandholm, 2007] Tuomas Sandholm. Expressive commerce and its application to sourcing: How we conducted $35 bil- lion of generalized combinatorial auctions. AI Magazine, 28(3):45-45, 2007.","title":"Expressive commerce and its application to sourcing: How we conducted $35 billion of generalized combinatorial auctions","authors":"Tuomas Sandholm, Sandholm","year":"2007","venue":"AI Magazine","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Vickrey, 1961] William Vickrey. Counterspeculation, auc- tions, and competitive sealed tenders. The Journal of Fi- nance, 16(1):8-37, 1961.","title":"Counterspeculation, auctions, and competitive sealed tenders","authors":"William Vickrey","year":"1961","venue":"The Journal of Finance","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}