{"id":856290,"date":"2022-06-27T14:32:27","date_gmt":"2022-06-27T21:32:27","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/"},"modified":"2022-06-27T14:32:27","modified_gmt":"2022-06-27T21:32:27","slug":"fair-shares-feasibility-domination-and-incentives","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/fair-shares-feasibility-domination-and-incentives\/","title":{"rendered":"Fair Shares: Feasibility, Domination and Incentives"},"content":{"rendered":"

We consider fair allocation of a set\u00a0M<\/span><\/span><\/span><\/span>\u00a0of indivisible goods to\u00a0n<\/span><\/span><\/span><\/span>\u00a0equally-entitled agents, with no monetary transfers. Every agent\u00a0i<\/span><\/span><\/span><\/span>\u00a0has a valuation\u00a0v<\/span>i<\/span><\/span><\/span><\/span><\/span>\u00a0from some given class of valuation functions. A share\u00a0s<\/span><\/span><\/span><\/span>\u00a0is a function that maps a pair\u00a0(<\/span>v<\/span>i<\/span><\/span>,<\/span>n<\/span>)<\/span><\/span><\/span><\/span>\u00a0to a value, with the interpretation that if an allocation of\u00a0M<\/span><\/span><\/span><\/span>\u00a0to\u00a0n<\/span><\/span><\/span><\/span>\u00a0agents fails to give agent\u00a0i<\/span><\/span><\/span><\/span>\u00a0a bundle of value at least equal to\u00a0s<\/span>(<\/span>v<\/span>i<\/span><\/span>,<\/span>n<\/span>)<\/span><\/span><\/span><\/span>, this serves as evidence that the allocation is not fair towards\u00a0i<\/span><\/span><\/span><\/span>. For such an interpretation to make sense, we would like the share to be feasible, meaning that for any valuations in the class, there is an allocation that gives every agent at least her share. The maximin share was a natural candidate for a feasible share for additive valuations. However, Kurokawa, Procaccia and Wang [2018] show that it is not feasible.<\/p>\n

We initiate a systematic study of the family of feasible shares. We say that a share is \\emph{self maximizing} if truth-telling maximizes the implied guarantee. We show that every feasible share is dominated by some self-maximizing and feasible share. We seek to identify those self-maximizing feasible shares that are polynomial time computable, and offer the highest share values. We show that a SM-dominating feasible share — one that dominates every self-maximizing (SM) feasible share — does not exist for additive valuations (and beyond). Consequently, we relax the domination property to that of domination up to a multiplicative factor of \u03c1<\/span><\/span><\/span><\/span>\u00a0(called\u00a0\u03c1<\/span><\/span><\/span><\/span>-dominating). For additive valuations we present shares that are feasible, self-maximizing and polynomial-time computable. For\u00a0n<\/span><\/span><\/span><\/span>\u00a0agents we present such a share that is\u00a02<\/span>n<\/span><\/span>3<\/span>n<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span>-dominating. For two agents we present such a share that is\u00a0(<\/span>1<\/span>\u2212<\/span>\u03f5<\/span>)<\/span><\/span><\/span><\/span>-dominating. Moreover, for these shares we present poly-time algorithms that compute allocations that give every agent at least her share.<\/p>\n","protected":false},"excerpt":{"rendered":"

We consider fair allocation of a set\u00a0M\u00a0of indivisible goods to\u00a0n\u00a0equally-entitled agents, with no monetary transfers. Every agent\u00a0i\u00a0has a valuation\u00a0vi\u00a0from some given class of valuation functions. A share\u00a0s\u00a0is a function that maps a pair\u00a0(vi,n)\u00a0to a value, with the interpretation that if an allocation of\u00a0M\u00a0to\u00a0n\u00a0agents fails to give agent\u00a0i\u00a0a bundle of value at least equal to\u00a0s(vi,n), this […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556,13548],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-856290","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-research-area-economics","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2022-5-22","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/2205.07519","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"Moshe Babaioff","user_id":33000,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Moshe Babaioff"},{"type":"text","value":"Uriel Feige","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[856077],"msr_group":[],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/856290"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/856290\/revisions"}],"predecessor-version":[{"id":856293,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/856290\/revisions\/856293"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=856290"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=856290"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=856290"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=856290"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=856290"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=856290"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=856290"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=856290"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=856290"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=856290"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=856290"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=856290"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=856290"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=856290"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=856290"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=856290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}