[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84079-en":3,"doc-seo-84079-105":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},84079,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Slack and Budget Breaking in Threshold Team Production","A threshold system completes a public task only after κ verifiable shares are publicly committed, and the honest schedule yields N⋆=κ+∆ share opportunities by deadline t⋆. Slack shares are redundant, so a coalition can delay completion iff it withholds at least ∆+1 shares. Agents earn a direct fee f per committed share, while coalition delay value is bounded by L and possible recovery-slot fee leakage by R+1. The principal posts a nonnegative completion bounty that depends only on committed shares and expires if late; full participation is ex-post strongly delay proof exactly when (∆+1)f+B≥L+R+1.","arXiv :2607 .06 197v 1 [ cs .GT] 7 Jul 2026  \nSlack and Budget Breaking in Threshold Team  \nProduction  \nBenjamin Marsh 1 ,2 and Alejandro Ranchal-Pedrosa 1  \n1 Sei Labs  \n2 University of Portsmouth  \n{[ben|alejandro}@seinetwork.io](ben|alejandro}@seinetwork.io)  \nAbstract. A threshold system completes a public task only after κ verifiable shares are publicly committed. If the honest schedule creates N⋆ = κ + ∆ share opportunities by deadline t⋆ , then ∆ shares areslack such that a coalition delays completion if and only if it withholdsat least ∆ + 1 shares. The incentive problem is therefore to price the cheapest sabotage set. Agents receive a direct fee f per committed share. A delaying coalition may also obtain delay value at most L, and may earn additional fee revenue during recovery after the deadline. Let R+1 bea pathwise upper bound on the coalition’s incremental fee revenue in a recovery slot that completes the task, including any same-slot overshoot. The principal can post a nonnegative completion bounty that depends only on committed shares, uses no deposits or punishments, and expires if completion is late. The optimal rule is uniform, as if completion occurs by t⋆ , every admissible horizon share receives B/N⋆ , otherwise no bounty is paid. Full participation is ex-post strongly delay proof exactly when (∆ + 1)f + ~~1~~ B ≥ L + R+1 . Equivalently, the exact worst-case budget is B ⋆ = 1 􀀀 L+R+1 −(∆+1)f 􀀁 + . The bound is tight for every nonnegative completion-measurable bounty, among the N⋆ horizon shares, some ∆+1 receive total bounty at most (∆ + 1)B/N⋆ , and withholding precisely those shares delays completion. The result applies to threshold signatures, data availability certification, coded dissemination, and generic k-of-n completion tasks. We also isolate a separate limit, no transfer rule based only on completed shares can remove a final slot race in which a coalition has already observed enough pre-completion shares to act.  \nKeywords: Mechanism design · Team production · Coalition proofness · Robust mechanism design · Blockchain incentives  \n2 B. Marsh and A. Ranchal-Pedrosa  \n1 Introduction  \nMany distributed systems complete a public task only after collecting a threshold number of verifiable shares. A certificate forms after enough validators sign. A data availability layer accepts a block after enough samples or attestations appear. A coded dissemination protocol reveals a payload after enough coded shares are publicly committed. A generic k-of-n protocol completes once enough votes or certificate shares are included [8–11, 22, 16] . In all of these cases, completion is not produced by one agent but by a threshold team. This creates a simple sabotage problem as the principal values timely completion, while individual agents receive local fees for their own shares. A coalition may prefer to withhold enough of its shares to push completion past the honest deadline. In blockchain applications, one source of such delay value is maximal extractable value (MEV): profit from transaction ordering, front-running, liquidations, arbitrage, or related use of preconfirmation information [17–19] . In the model we do not need the source of the value. We only require an upper bound L on the coalition’s redistributable gain from delay. Modelling the game as running in a series of slots that accumulate shares, let t⋆ be the honest horizon, the first slot by which the threshold would be reached if all available agents submitted their shares. If the honest schedule creates N⋆ = κ + ∆ share opportunities by this horizon, then ∆ shares are redundant. If a coalition withholds W horizon shares, completion is delayed if and only if W > ∆ . Thus zero slack is a knife edge such that one missing share delays completion. Positive slack changes the strategic problem. The first ∆ withholdings do not delay anything unless they are coordinated with at least one more withholding. Slack converts unilateral free riding into coordinated s","cbCaivAZfgG3O4tx","https://ap.wps.com/l/cbCaivAZfgG3O4tx","pdf",541066,3,1,23,"English","en",105,"# Introduction\n## Threshold completion and slack\n## Coalition-proof delay and robust mechanism design\n## TIMELY-TEAM bounty rule and budget condition","[{\"question\":\"What determines whether a coalition can delay task completion in this threshold model?\",\"answer\":\"Completion is delayed iff the coalition withholds at least ∆+1 horizon shares when the honest schedule creates N⋆=κ+∆ opportunities by deadline t⋆.\"},{\"question\":\"How are agents rewarded and what additional value can the coalition gain from delaying?\",\"answer\":\"Agents receive a direct fee f per committed share. A delaying coalition may also obtain delay value up to L and can capture incremental fee revenue during recovery after the deadline, bounded by R+1.\"},{\"question\":\"What is the optimal completion bounty mechanism and its exact budget requirement?\",\"answer\":\"The optimal rule is a uniform timely-team bounty: if completion happens by t⋆ each admissible horizon share gets B/N⋆, otherwise the bounty expires. Full participation is ex-post strongly delay proof exactly when (∆+1)f + B ≥ L + R+1, equivalently the worst-case budget is B⋆= (1 − (L+R+1)/((∆+1)f?))^+ form as stated in the paper.\"}]",1784192580,58,{"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},"slack-and-budget-breaking-in-threshold-team-production","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/slack-and-budget-breaking-in-threshold-team-production/84079/",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","2026-07-23","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 determines whether a coalition can delay task completion in this threshold model?","Question",{"text":75,"@type":76},"Completion is delayed iff the coalition withholds at least ∆+1 horizon shares when the honest schedule creates N⋆=κ+∆ opportunities by deadline t⋆.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are agents rewarded and what additional value can the coalition gain from delaying?",{"text":80,"@type":76},"Agents receive a direct fee f per committed share. A delaying coalition may also obtain delay value up to L and can capture incremental fee revenue during recovery after the deadline, bounded by R+1.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the optimal completion bounty mechanism and its exact budget requirement?",{"text":84,"@type":76},"The optimal rule is a uniform timely-team bounty: if completion happens by t⋆ each admissible horizon share gets B/N⋆, otherwise the bounty expires. Full participation is ex-post strongly delay proof exactly when (∆+1)f + B ≥ L + R+1, equivalently the worst-case budget is B⋆= (1 − (L+R+1)/((∆+1)f?))^+ form as stated in the paper.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]