[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84545-en":3,"doc-seo-84545-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84545,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Fully Distributed Tâtonnement for Chores Markets","We study price-adjustment dynamics for computing competitive equilibria in Fisher markets with chores, where prices act as payments for taking undesirable tasks. Classical excess-demand dynamics may fail, and even Walrasian tâtonnement can diverge. Prior relative tâtonnement restores convergence by subtracting the average excess-demand signal, but it couples updates across all chores. We show multiplicative tâtonnement is fully distributed: each chore price updates using only its own current price and excess-demand signal, and converges to a CE for continuous convex 1-homogeneous disutilities.","Fully Distributed Tâtonnement for Chores Markets  \nBhaskar Ray Chaudhury  \nUniversity of Illinois Urbana-Champaign  \nRuta Mehta  \nUniversity of Illinois Urbana-Champaign  \nChristian Kroer  \nColumbia University  \nTianlong Nan  \nColumbia University  \narXiv :2607 .00300v 1 [ cs .GT] 1 Jul 2026  \nAbstract  \nWe study price-adjustment dynamics for computing competitive equilibria (CE) in Fisher markets with chores. Unlike in classical goods markets, prices in chores markets are payments for taking on undesirable tasks, and natural excess-demand dynamics can fail; even the naïve analogue of Walrasian tâtonnement may diverge.  \nRecent work of [12] overcomes this obstacle via relative tâtonnement, which subtracts the average excess-demand signal from the excess demand vector. This recovers convergence, but at the cost of coupling the price updates across all chores.  \nThis leaves open whether such global coupling is inherent, or whether convergent tâtonnement can be recovered through a genuinely local update in which each chore reacts only to its own excess demand.  \nWe answer this question affirmatively through multiplicative tâtonnement, a fully distributed dynamics in which each chore price is updated using only its current price and its own excess-demand signal. Although the update contains no explicit normalization term, Walras’ law and the multiplicative form of the update implicitly preserve the relevant aggregate price geometry. We prove that multiplicative tâtonnement converges to a CE in any chores Fisher market with continuous, convex, and 1-homogeneous (CCH) disutilities. For convex CES disutilities, we further prove an approximate-CE convergence rate with the same O(1/ε2 ) dependence as relative tâtonnement, but with improved dependence on problem constants. Experiments on real-world and simulated instances show that multiplicative tâtonnementis substantially faster in practice, often by an order of magnitude.  \n1 Introduction  \nCompetitive equilibrium (CE) is one of the central solution concepts in market design and microeconomic theory. The Fisher market is one of the most fundamental market settings. In a classical Fisher market with goods, there is a set of m goods and n agents. Each agent is endowed with a fixed budget of money, and once prices are assigned to the goods, agents spend their budgets to obtain utility-maximizing bundles. Prices are at equilibrium when these individual demands exactly clear the market. Beyond the static existence and welfare properties of CE, a classical question asks whether natural market dynamics can find such prices. Walrasian tâtonnement is the canonical example: prices are adjusted in response to excess demand, increasing when demand exceeds supply and decreasing when supply exceeds demand [46] . The stability and convergence of such dynamics have been studied since the foundational work of [43, 3, 2], and remain active topics in algorithmic game theory [19, 20, 15, 31, 40] .  \nThis paper studies tâtonnement dynamics in Fisher markets with chores. In a chores market, agents do not pay to receive goods; rather, they are paid to perform undesirable tasks. Thus prices represent payments per unit of work, and the natural response to imbalance is reversed: when a chore is under-demanded, its price should increase to attract agents, while an over-demanded chore should  \nPreprint. Under review.  \nbecome less lucrative. This reversal leads to a substantially different dynamical landscape. Chores markets can have disconnected sets of equilibria, and excess demand no longer has the monotonic structure that supports many goods-market analyses. Correspondingly, the computational literature on chores and mixed manna deals with non-convex optimization issues and is more nuanced than in the goods case [6, 29, 7, 10, 9, 11] .  \nRelative Tâtonnement. The recent work of [12] initiated the study of tâtonnement dynamics for chores markets. They show that the naïve additive analogue of tâtonnement can d","cbCaiaHcF8kf5oA1","https://ap.wps.com/l/cbCaiaHcF8kf5oA1","pdf",621706,1,21,"English","en",105,"# Abstract\n# Introduction\n## Competitive equilibrium and Walrasian tâtonnement\n## Fisher markets with chores\n## Relative tâtonnement\n## The case for decoupled price adjustment dynamics\n# Multiplicative tâtonnement","[{\"question\":\"What makes tâtonnement challenging in Fisher markets with chores?\",\"answer\":\"In chores markets, prices are payments for taking undesirable tasks, so the imbalance response is reversed and the usual monotonic structure supporting goods-market analyses may not hold. As a result, excess-demand dynamics—and even the naive Walrasian analogue—can diverge.\"},{\"question\":\"How does relative tâtonnement recover convergence, and why is it not fully distributed?\",\"answer\":\"Relative tâtonnement subtracts the average excess-demand signal from each coordinate to restore convergence. This requires each price update to use excess-demand signals from all other chores, creating global coupling rather than decentralization.\"},{\"question\":\"What is multiplicative tâtonnement, and what convergence guarantee does it provide?\",\"answer\":\"Multiplicative tâtonnement updates each chore price using only its current price and its own excess-demand signal, without an explicit normalization term. The paper proves convergence to a competitive equilibrium in any chores Fisher market with continuous, convex, and 1-homogeneous (CCH) disutilities, and provides an approximate-CE rate for convex CES disutilities.\"}]",1784196571,53,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"fully-distributed-tatonnement-for-chores-markets","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/fully-distributed-tatonnement-for-chores-markets/84545/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What makes tâtonnement challenging in Fisher markets with chores?","Question",{"text":74,"@type":75},"In chores markets, prices are payments for taking undesirable tasks, so the imbalance response is reversed and the usual monotonic structure supporting goods-market analyses may not hold. As a result, excess-demand dynamics—and even the naive Walrasian analogue—can diverge.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does relative tâtonnement recover convergence, and why is it not fully distributed?",{"text":79,"@type":75},"Relative tâtonnement subtracts the average excess-demand signal from each coordinate to restore convergence. This requires each price update to use excess-demand signals from all other chores, creating global coupling rather than decentralization.",{"name":81,"@type":72,"acceptedAnswer":82},"What is multiplicative tâtonnement, and what convergence guarantee does it provide?",{"text":83,"@type":75},"Multiplicative tâtonnement updates each chore price using only its current price and its own excess-demand signal, without an explicit normalization term. The paper proves convergence to a competitive equilibrium in any chores Fisher market with continuous, convex, and 1-homogeneous (CCH) disutilities, and provides an approximate-CE rate for convex CES disutilities.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]