{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T23:04:08Z","timestamp":1762211048589,"version":"3.40.3"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031432538"},{"type":"electronic","value":"9783031432545"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-43254-5_17","type":"book-chapter","created":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T23:04:03Z","timestamp":1693782243000},"page":"290-307","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Frontier of\u00a0Intractability for\u00a0EFX with\u00a0Two Agents"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5436-7890","authenticated-orcid":false,"given":"Paul W.","family":"Goldberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-2642","authenticated-orcid":false,"given":"Kasper","family":"H\u00f8gh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5255-9349","authenticated-orcid":false,"given":"Alexandros","family":"Hollender","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,4]]},"reference":[{"doi-asserted-by":"publisher","unstructured":"Akrami, H., Alon, N., Chaudhury, B.R., Garg, J., Mehlhorn, K., Mehta, R.: EFX: a simpler approach and an (almost) optimal guarantee via rainbow cycle number. In: Proceedings of the 24th ACM Conference on Economics and Computation (EC), p. 61 (2023). https:\/\/doi.org\/10.1145\/3580507.3597799","key":"17_CR1","DOI":"10.1145\/3580507.3597799"},{"doi-asserted-by":"publisher","unstructured":"Amanatidis, G., et al.: Fair division of indivisible goods: recent progress and open questions. Artif. Intell. 322 (2023). https:\/\/doi.org\/10.1016\/j.artint.2023.103965","key":"17_CR2","DOI":"10.1016\/j.artint.2023.103965"},{"key":"17_CR3","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.tcs.2021.02.020","volume":"863","author":"G Amanatidis","year":"2021","unstructured":"Amanatidis, G., Birmpas, G., Filos-Ratsikas, A., Hollender, A., Voudouris, A.A.: Maximum Nash welfare and other stories about EFX. Theoret. Comput. Sci. 863, 69\u201385 (2021). https:\/\/doi.org\/10.1016\/j.tcs.2021.02.020","journal-title":"Theoret. Comput. Sci."},{"doi-asserted-by":"publisher","unstructured":"Amanatidis, G., Birmpas, G., Lazos, P., Leonardi, S., Reiffenh\u00e4user, R.: Round-robin beyond additive agents: Existence and fairness of approximate equilibria. In: Proceedings of the 24th ACM Conference on Economics and Computation (EC), pp. 67\u201387 (2023). https:\/\/doi.org\/10.1145\/3580507.3597796","key":"17_CR4","DOI":"10.1145\/3580507.3597796"},{"doi-asserted-by":"publisher","unstructured":"Aziz, H., Mackenzie, S.: A discrete and bounded envy-free cake cutting protocol for any number of agents. In: Proceedings of the 57th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 416\u2013427 (2016). https:\/\/doi.org\/10.1109\/focs.2016.52","key":"17_CR5","DOI":"10.1109\/focs.2016.52"},{"doi-asserted-by":"crossref","unstructured":"Babaioff, M., Ezra, T., Feige, U.: Fair and truthful mechanisms for dichotomous valuations. In: Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pp. 5119\u20135126 (2021). https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/16647","key":"17_CR6","DOI":"10.1609\/aaai.v35i6.16647"},{"doi-asserted-by":"publisher","unstructured":"Barman, S., Krishnamurthy, S.K., Vaish, R.: Finding fair and efficient allocations. In: Proceedings of the 19th ACM Conference on Economics and Computation (EC), pp. 557\u2013574 (2018). https:\/\/doi.org\/10.1145\/3219166.3219176","key":"17_CR7","DOI":"10.1145\/3219166.3219176"},{"doi-asserted-by":"publisher","unstructured":"Berger, B., Cohen, A., Feldman, M., Fiat, A.: Almost full EFX exists for four agents. In: Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI), pp. 4826\u20134833 (2022). https:\/\/doi.org\/10.1609\/aaai.v36i5.20410","key":"17_CR8","DOI":"10.1609\/aaai.v36i5.20410"},{"issue":"6","key":"17_CR9","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1086\/664613","volume":"119","author":"E Budish","year":"2011","unstructured":"Budish, E.: The combinatorial assignment problem: approximate competitive equilibrium from equal incomes. J. Polit. Econ. 119(6), 1061\u20131103 (2011). https:\/\/doi.org\/10.1086\/664613","journal-title":"J. Polit. Econ."},{"doi-asserted-by":"publisher","unstructured":"Caragiannis, I., Gravin, N., Huang, X.: Envy-freeness up to any item with high Nash welfare: the virtue of donating items. In: Proceedings of the 20th ACM Conference on Economics and Computation (EC), pp. 527\u2013545 (2019). https:\/\/doi.org\/10.1145\/3328526.3329574","key":"17_CR10","DOI":"10.1145\/3328526.3329574"},{"doi-asserted-by":"publisher","unstructured":"Caragiannis, I., Kurokawa, D., Moulin, H., Procaccia, A.D., Shah, N., Wang, J.: The unreasonable fairness of maximum Nash welfare. ACM Trans. Econ. Comput. 7(3), 12:1\u201312:32 (2019). https:\/\/doi.org\/10.1145\/3355902","key":"17_CR11","DOI":"10.1145\/3355902"},{"doi-asserted-by":"publisher","unstructured":"Chaudhury, B.R., Garg, J., Mehlhorn, K.: EFX exists for three agents. In: Proceedings of the 21st ACM Conference on Economics and Computation (EC), pp. 1\u201319 (2020). https:\/\/doi.org\/10.1145\/3391403.3399511","key":"17_CR12","DOI":"10.1145\/3391403.3399511"},{"doi-asserted-by":"publisher","unstructured":"Chaudhury, B.R., Garg, J., Mehlhorn, K., Mehta, R., Misra, P.: Improving EFX guarantees through rainbow cycle number. In: Proceedings of the 22nd ACM Conference on Economics and Computation (EC), pp. 310\u2013311 (2021). https:\/\/doi.org\/10.1145\/3465456.3467605","key":"17_CR13","DOI":"10.1145\/3465456.3467605"},{"issue":"4","key":"17_CR14","doi-asserted-by":"publisher","first-page":"1336","DOI":"10.1137\/20m1359134","volume":"50","author":"BR Chaudhury","year":"2021","unstructured":"Chaudhury, B.R., Kavitha, T., Mehlhorn, K., Sgouritsa, A.: A little charity guarantees almost envy-freeness. SIAM J. Comput. 50(4), 1336\u20131358 (2021). https:\/\/doi.org\/10.1137\/20m1359134","journal-title":"SIAM J. Comput."},{"issue":"1","key":"17_CR15","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/bf01584082","volume":"1","author":"J Edmonds","year":"1971","unstructured":"Edmonds, J.: Matroids and the greedy algorithm. Math. Program. 1(1), 127\u2013136 (1971). https:\/\/doi.org\/10.1007\/bf01584082","journal-title":"Math. Program."},{"unstructured":"Foley, D.K.: Resource Allocation and the Public Sector. Ph.D. thesis, Yale University (1966)","key":"17_CR16"},{"issue":"2","key":"17_CR17","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1016\/s0021-9800(68)80039-0","volume":"4","author":"D Gale","year":"1968","unstructured":"Gale, D.: Optimal assignments in an ordered set: an application of matroid theory. J. Comb. Theory 4(2), 176\u2013180 (1968). https:\/\/doi.org\/10.1016\/s0021-9800(68)80039-0","journal-title":"J. Comb. Theory"},{"unstructured":"Gamow, G., Stern, M.: Puzzle-Math. Viking Press (1958)","key":"17_CR18"},{"doi-asserted-by":"publisher","unstructured":"Gourv\u00e8s, L., Monnot, J., Tlilane, L.: Near fairness in matroids. In: Proceedings of the 21st European Conference on Artificial Intelligence (ECAI), pp. 393\u2013398 (2014). https:\/\/doi.org\/10.3233\/978-1-61499-419-0-393","key":"17_CR19","DOI":"10.3233\/978-1-61499-419-0-393"},{"doi-asserted-by":"crossref","unstructured":"Gul, F., Stacchetti, E.: Walrasian equilibrium with gross substitutes. J. Econ. Theory 87(1), 95\u2013124 (1999). https:\/\/EconPapers.repec.org\/RePEc:eee:jetheo:v:87:y:1999:i:1:p:95-124","key":"17_CR20","DOI":"10.1006\/jeth.1999.2531"},{"issue":"1","key":"17_CR21","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0022-0000(88)90046-3","volume":"37","author":"DS Johnson","year":"1988","unstructured":"Johnson, D.S., Papadimitriou, C.H., Yannakakis, M.: How easy is local search? J. Comput. Syst. Sci. 37(1), 79\u2013100 (1988). https:\/\/doi.org\/10.1016\/0022-0000(88)90046-3","journal-title":"J. Comput. Syst. Sci."},{"issue":"2","key":"17_CR22","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.geb.2005.02.006","volume":"55","author":"B Lehmann","year":"2006","unstructured":"Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. Games Econom. Behav. 55(2), 270\u2013296 (2006). https:\/\/doi.org\/10.1016\/j.geb.2005.02.006","journal-title":"Games Econom. Behav."},{"doi-asserted-by":"publisher","unstructured":"Lipton, R.J., Markakis, E., Mossel, E., Saberi, A.: On approximately fair allocations of indivisible goods. In: Proceedings of the 5th ACM Conference on Electronic Commerce (EC), pp. 125\u2013131 (2004). https:\/\/doi.org\/10.1145\/988772.988792","key":"17_CR23","DOI":"10.1145\/988772.988792"},{"issue":"2","key":"17_CR24","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1137\/20m1353381","volume":"35","author":"P Manurangsi","year":"2021","unstructured":"Manurangsi, P., Suksompong, W.: Closing gaps in asymptotic fair division. SIAM J. Discret. Math. 35(2), 668\u2013706 (2021). https:\/\/doi.org\/10.1137\/20m1353381","journal-title":"SIAM J. Discret. Math."},{"issue":"2","key":"17_CR25","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0304-3975(91)90200-L","volume":"81","author":"N Megiddo","year":"1991","unstructured":"Megiddo, N., Papadimitriou, C.H.: On total functions, existence theorems and computational complexity. Theoret. Comput. Sci. 81(2), 317\u2013324 (1991). https:\/\/doi.org\/10.1016\/0304-3975(91)90200-L","journal-title":"Theoret. Comput. Sci."},{"key":"17_CR26","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1016\/j.geb.2017.10.016","volume":"106","author":"R Paes Leme","year":"2017","unstructured":"Paes Leme, R.: Gross substitutability: an algorithmic survey. Games Econom. Behav. 106, 294\u2013316 (2017). https:\/\/doi.org\/10.1016\/j.geb.2017.10.016","journal-title":"Games Econom. Behav."},{"issue":"2","key":"17_CR27","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1137\/19m124397x","volume":"34","author":"B Plaut","year":"2020","unstructured":"Plaut, B., Roughgarden, T.: Almost envy-freeness with general valuations. SIAM J. Discret. Math. 34(2), 1039\u20131068 (2020). https:\/\/doi.org\/10.1137\/19m124397x","journal-title":"SIAM J. Discret. Math."},{"doi-asserted-by":"publisher","unstructured":"Rado, R.: Note on independence functions. Proc. Lond. Math. Soc. s3-7(1), 300\u2013320 (1957). https:\/\/doi.org\/10.1112\/plms\/s3-7.1.300","key":"17_CR28","DOI":"10.1112\/plms\/s3-7.1.300"},{"unstructured":"Steinhaus, H.: The problem of fair division. Econometrica 16(1), 101\u2013104 (1948). https:\/\/www.jstor.org\/stable\/1914289","key":"17_CR29"},{"doi-asserted-by":"publisher","unstructured":"Steinhaus, H.: Sur la division pragmatique. Econometrica 17(Suppl.), 315\u2013319 (1949). https:\/\/doi.org\/10.2307\/1907319","key":"17_CR30","DOI":"10.2307\/1907319"},{"issue":"8","key":"17_CR31","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1080\/00029890.1980.11995109","volume":"87","author":"W Stromquist","year":"1980","unstructured":"Stromquist, W.: How to cut a cake fairly. Am. Math. Mon. 87(8), 640\u2013644 (1980). https:\/\/doi.org\/10.1080\/00029890.1980.11995109","journal-title":"Am. Math. Mon."},{"issue":"10","key":"17_CR32","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1080\/00029890.1999.12005142","volume":"106","author":"FE Su","year":"1999","unstructured":"Su, F.E.: Rental harmony: Sperner\u2019s lemma in fair division. Am. Math. Mon. 106(10), 930\u2013942 (1999). https:\/\/doi.org\/10.1080\/00029890.1999.12005142","journal-title":"Am. Math. Mon."},{"issue":"1","key":"17_CR33","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0022-0531(74)90075-1","volume":"9","author":"HR Varian","year":"1974","unstructured":"Varian, H.R.: Equity, envy, and efficiency. J. Econ. Theory 9(1), 63\u201391 (1974). https:\/\/doi.org\/10.1016\/0022-0531(74)90075-1","journal-title":"J. Econ. Theory"},{"issue":"1","key":"17_CR34","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0022-247x(80)90225-5","volume":"78","author":"DR Woodall","year":"1980","unstructured":"Woodall, D.R.: Dividing a cake fairly. J. Math. Anal. Appl. 78(1), 233\u2013247 (1980). https:\/\/doi.org\/10.1016\/0022-247x(80)90225-5","journal-title":"J. Math. Anal. Appl."}],"container-title":["Lecture Notes in Computer Science","Algorithmic Game Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-43254-5_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T23:15:54Z","timestamp":1693782954000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-43254-5_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031432538","9783031432545"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-43254-5_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"4 September 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SAGT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Algorithmic Game Theory","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Egham","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 September 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sagt2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"OpenReview","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"59","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"26","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"44% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}