[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83440-en":3,"doc-seo-83440-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83440,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","From Welfare to Utility: Generalized Objectives in Budget-Feasible Procurement","This work studies mechanism design for the budget-feasible procurement problem, where a buyer must obtain goods or services from multiple strategic sellers with private production costs, while respecting an overall budget for payments. It develops optimal and approximately optimal mechanisms targeting buyer utility, welfare, and objective generalizations. For welfare, it gives a simple constant-factor approximation in prior-free settings. In Bayesian settings, it first achieves utility optimality with budget constraints in expectation, then enforces ex-post budget feasibility while preserving near-optimal utility guarantees.","arXiv :2607 .00101v1 [ cs .GT] 30 Jun 2026  \nFrom Welfare to Utility: Generalized Objectives in Budget-Feasible  \nProcurement ∗  \nAlon Eden † Eldar Kerner ‡ Kira Goldner§ Thodoris Tsilivis ¶  \nJuly 2, 2026  \nAbstract  \nWe study mechanism design for the budget-feasible procurement problem, a natural problem that arises when a buyer wants to procure goods or services from multiple strategic sellers who each have a cost to provide that service, the buyer has a value for each service procured, but is constrained by a budget. In contrast to prior work, which has focused on buyer value maximization for this problem, we solve for optimal and approximately-optimal mechanisms for the objectives of buyer utility (value of procured services minus payments), welfare (value minus production costs), and generalizations of the two. For welfare, we design a simple mechanism that obtains a constant-factor approximation for the prior-free (worst-case) setting. As prior-free mechanisms fail to provide any guarantee for utility, even for a single seller, we consider Bayesian settings, where the buyer has distributional knowledge over sellers’ costs. We first provide a utility-optimal mechanism that satisfies the buyer’s budget constraint in expectation, then we show how to modify the mechanism to satisfy the budget constraint ex-post, for every realization of seller costs, while still obtaining near-optimal utility guarantees. Finally, we generalize our mechanisms to other objectives.  \n∗ The work of A. Eden and E. Kerner was supported by the Israel Science Foundation (grant No. 533/23) . Alon Eden is the Incumbent of the Harry & Abe Sherman Senior Lectureship at the School of Computer Science and Engineering at the Hebrew University. The work of K. Goldner and T. Tsilivis was supported by NSF CAREER Award CCF-2441071 .  \n†Hebrew University; [alon.eden@mail.huji.ac.il](alon.eden@mail.huji.ac.il).  \n‡Hebrew University; [eldar.kerner@mail.huji.ac.il](eldar.kerner@mail.huji.ac.il).  \n§ Boston University; [goldner@bu.edu](goldner@bu.edu).  \n¶ Boston University; [tsilivis@bu.edu](tsilivis@bu.edu).  \n1 Introduction  \nConsider a company that wishes to procure compute from some of n possible sellers. The buyer has some value vi for each compute contract that they procure depending on the seller i. However, each seller also has their own private cost ci to supply compute—e.g., due to electricity, hardware usage, and system maintenance. Finally, the buyer has a budget B that they have set aside for spending on compute, and the sum of payments that they make to the sellers cannot exceed this budget.  \nThis is the budget-feasible procurement problem, relevant in any scenario where a buyer seeks to procure goods or services from self-interested sellers and is constrained by a budget. Such a scenario arises in many settings relevant in today’s modern computing ecosystem:  \n• Online crowdsourcing task: a requester in Mechanical Turk seeks to procure taskers subject to some budget [Anari et al. , 2014; Balkanski and Hartline, 2016; Singla and Krause, 2013; Singer and Mittal, 2013] .  \n• API access to language models: a user wants to access specialized language models through an Application Programming Interface (API) to perform a task, where every access to the API is monetized by the company training the language model [Bhawalkar et al. , 2025a] .  \n• Distributed/Federated learning: a model trainer wants to purchase models trained locally by users on their private data in order to train a global model [Zhang et al. , 2021] .  \nThis problem was first introduced by Singer [2010] and has since been extensively studied in algorithmic mechanism design, receiving particular attention from researchers at large technology platforms [Deng et al. , 2025; Anari et al. , 2018; Bei et al. , 2012; Bhawalkar et al. , 2025a; Chen et al. , 2011] . However, the vast majority of work focuses only on the objective of value maximization. The justification is that the buyer has set ","cbCaiu4YSoGnBEe0","https://ap.wps.com/l/cbCaiu4YSoGnBEe0","pdf",778821,2,1,37,"English","en",105,"# Abstract\n# Introduction\n## Problem Setting and Motivation\n## Objectives: Utility, Welfare, and Generalizations","[{\"question\":\"What is the budget-feasible procurement problem studied in the paper?\",\"answer\":\"A buyer wants to procure goods or services from multiple strategic sellers, each with a private cost, while the buyer’s payments must not exceed a fixed budget.\"},{\"question\":\"How does the paper differ from prior work on this problem?\",\"answer\":\"Prior work mainly focuses on maximizing buyer value under budget constraints, while this paper investigates mechanisms for buyer utility, welfare, and generalized objectives.\"},{\"question\":\"What mechanisms are proposed for welfare and for utility in Bayesian settings?\",\"answer\":\"For welfare, the paper designs a simple mechanism achieving a constant-factor approximation in prior-free settings. For utility in Bayesian settings, it first satisfies the budget constraint in expectation, then modifies the mechanism to satisfy the budget constraint ex-post for every cost realization while retaining near-optimal utility guarantees.\"}]",1784187736,93,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"from-welfare-to-utility-generalized-objectives-in-budget-feasible-procurement","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/from-welfare-to-utility-generalized-objectives-in-budget-feasible-procurement/83440/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the budget-feasible procurement problem studied in the paper?","Question",{"text":75,"@type":76},"A buyer wants to procure goods or services from multiple strategic sellers, each with a private cost, while the buyer’s payments must not exceed a fixed budget.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper differ from prior work on this problem?",{"text":80,"@type":76},"Prior work mainly focuses on maximizing buyer value under budget constraints, while this paper investigates mechanisms for buyer utility, welfare, and generalized objectives.",{"name":82,"@type":73,"acceptedAnswer":83},"What mechanisms are proposed for welfare and for utility in Bayesian settings?",{"text":84,"@type":76},"For welfare, the paper designs a simple mechanism achieving a constant-factor approximation in prior-free settings. 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