{"id":185735,"date":"2010-08-11T00:00:00","date_gmt":"2010-12-28T09:39:10","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/optimal-auctions-with-budget-constraints\/"},"modified":"2016-08-22T11:28:00","modified_gmt":"2016-08-22T18:28:00","slug":"optimal-auctions-with-budget-constraints","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/optimal-auctions-with-budget-constraints\/","title":{"rendered":"Optimal Auctions with Budget Constraints"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We consider an environment where potential buyers of an indivisible good have<br \/>\nliquidity constraints, in that they cannot pay more than their `budget&#8217;<br \/>\nregardless of their valuation. A buyer&#8217;s valuation for the good as well as her<br \/>\nbudget are her private information. We derive constrained-efficient and revenue<br \/>\nmaximizing auctions for this setting. In general, the optimal auction<br \/>\nrequires \u2018pooling\u2019 both at the top and in the middle despite the maintained<br \/>\nassumption of a monotone hazard rate. Further, the auctioneer will never find<br \/>\nit desirable to offer lump sum subsidies to bidders with low budgets.<\/p>\n<p>On a technical note, our analysis is based on the `reduced form\u2019 representation of auctions, which enables one to exploit a polymatroid representation of auctions. This polymatroid representation is useful in other applications, time permitting, will be outlined.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider an environment where potential buyers of an indivisible good have liquidity constraints, in that they cannot pay more than their `budget&#8217; regardless of their valuation. A buyer&#8217;s valuation for the good as well as her budget are her private information. We derive constrained-efficient and revenue maximizing auctions for this setting. In general, the [&hellip;]<\/p>\n","protected":false},"featured_media":280814,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[13561,13548],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-185735","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-research-area-economics","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/HvKNv5jNlaY","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185735"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/185735\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/280814"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=185735"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=185735"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=185735"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=185735"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=185735"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=185735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}