{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:47:41Z","timestamp":1760060861684,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:00:00Z","timestamp":1759968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72274062"],"award-info":[{"award-number":["72274062"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>In this paper, we study the multidimensional claims problem and introduce the eating algorithm to this problem. It is shown that a solution is efficient if and only if it is the outcome of the eating algorithm with a profile of specific eating functions. Moreover, we adapt three classical solutions, i.e., the constrained equal awards rule, constrained equal losses rule, and proportional rule, to the current setting and show that they are special cases of the eating algorithm with specific eating functions.<\/jats:p>","DOI":"10.3390\/g16050051","type":"journal-article","created":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T07:56:29Z","timestamp":1759996589000},"page":"51","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Solutions to Multidimensional Claims Problem"],"prefix":"10.3390","volume":"16","author":[{"given":"Sijia","family":"Xu","sequence":"first","affiliation":[{"name":"East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Liu","sequence":"additional","affiliation":[{"name":"East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1007\/s10479-021-04470-w","article-title":"Multi-issue bankruptcy problems with crossed claims","volume":"318","author":"Acosta","year":"2022","journal-title":"Annals of Operations Research"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1006\/jeth.2000.2710","article-title":"A new solution to the random assignment problem","volume":"100","author":"Bogomolnaia","year":"2001","journal-title":"Journal of Economic Theory"},{"key":"ref_3","unstructured":"Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. (2022). Introduction to algorithms, MIT Press. [4th ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"111932","DOI":"10.1016\/j.econlet.2024.111932","article-title":"Packaging for allocation","volume":"243","author":"Liu","year":"2024","journal-title":"Economics Letters"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0165-4896(82)90029-4","article-title":"A problem of rights arbitration from the Talmud","volume":"2","year":"1982","journal-title":"Mathematical Social Sciences"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0165-4896(02)00070-7","article-title":"Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: A survey","volume":"45","author":"Thomson","year":"2003","journal-title":"Mathematical Social Sciences"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.mathsocsci.2014.09.002","article-title":"Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update","volume":"74","author":"Thomson","year":"2015","journal-title":"Mathematical Social Sciences"}],"container-title":["Games"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4336\/16\/5\/51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:50:46Z","timestamp":1760035846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4336\/16\/5\/51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,9]]},"references-count":7,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["g16050051"],"URL":"https:\/\/doi.org\/10.3390\/g16050051","relation":{},"ISSN":["2073-4336"],"issn-type":[{"value":"2073-4336","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,9]]}}}