[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86409-en":3,"doc-seo-86409-105":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},86409,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Entropy Bounds for Local Coordination and Graph Amenability","Studies local pure coordination games on finite graphs where each vertex chooses between two symmetric actions using only local information, and the cost is the average edge disagreement. Prior work showed efficient coordination implies graph amenability (hyperfiniteness), but the quantitative bound suffered a square-root loss. This work improves the bound in the unbiased binary case by linking players’ local outputs to information measures ordered by information sources and controlling their distance via binary entropy. The result yields an amenability parameter of order εlog(1/ε) and shows the square-root loss is essentially unavoidable beyond binary profiles.","arXiv :2606 .0 1963v 3 [ cs .GT] 11 Jul 2026  \nEntropy Bounds for Local Coordination and Graph Amenability  \nRon Peretz∗ Dean Kraizberg†  \nJuly 14, 2026  \nAbstract  \nWe study local pure coordination games on finite graphs. In these games, each vertex must choose one of two symmetric actions using only local information, and the cost is the average disagreement across edges. Hutchcroft, Rospuskova, and Tamuz [1] showed that if such local coordination can be achieved with low cost, then the underlying graph must be amenable, or hyperfinite, but their quantitative bound has a square root loss.  \nWe improve this loss in the unbiased binary setting. The main idea is to associate with each player’s local output a probability measure that records, along an ordered list of information sources, the mutual information with that output. For binary outputs, two players who usually agree have nearby associated measures, with a bound given by the binary entropy of their disagreement probability. Combining this estimate with a grand coupling theorem yields an improved amenability bound of order εlog(1/ε), where ε is the average disagreement. We also show that the square root loss in the earlier general theorem is essentially unavoidable for nonbinary coordination profiles. Thus the binary assumption is not merely technical: it is what makes the improved entropy bound possible.  \nKeywords: Coordination Games, Information Games, Amenability, Social Networks.  \n1 Introduction  \nPure coordination problems involve a choice between alternatives that are a priori symmetric, where the only goal is to match the choices of others. Typical examples include choosing a convention, a standard, or a shared terminology. When agents are placed on a social network, the natural objective is local: each agent wants to coordinate with her neighbors. If all agents have access to a common global random signal, perfect coordination is immediate. The problem becomes substantially more interesting when information is local, so that each agent can base her action only on signals available within a bounded communication range.  \nHutchcroft, Rospuskova, and Tamuz [1] recently showed that the possibility of efficient local coordination is governed by the geometry of the underlying graph. Their notion of amenability, better known in the math literature as hyperfiniteness, means roughly that the graph can be partitioned into bounded local communities after deleting only a small fraction of edges. Such a partition immediately gives a simple leader construction: each community follows a leader whose signal is available to all members, and disagreement occurs only across the deleted edges. Thus amenability is sufficient for efficient coordination.  \nThe main result of Hutchcroft, Rospuskova, and Tamuz (HRT) is a converse: if local coordination is possible with low inefficiency, then the graph must be amenable. More precisely, in their  \n∗ Economics Department, Bar Ilan University, [Israel. ron.peretz@biu.ac.il](Israel. ron.peretz@biu.ac.il)[ ](Israel. ron.peretz@biu.ac.il)†School of Mathematical Sciences, Tel Aviv University, [deank@mail.tau.ac.il](deank@mail.tau.ac.il)  \nradius r model, if the average inefficiency is at most ε, then the graph is amenable with parameter of order √ε . Their proof proceeds through a more general probabilistic statement. Given local random variables with small average squared disagreement along edges, they construct a leader profile whose cost is controlled by the square root of the original cost. The construction associates with each local output a Shapley influence distribution over the available information sources and then uses a grand coupling theorem to choose leaders consistently across adjacent vertices.  \nIn this paper we improve the quantitative converse in the unbiased binary setting. We introduce the notion of an information skeleton, which separates the information constraints from the graph on which disagreements are measured. In t","cbCaicxoNyLcYYT1","https://ap.wps.com/l/cbCaicxoNyLcYYT1","pdf",418334,3,1,13,"English","en",105,"# Abstract\n# 1 Introduction\n## Local coordination on graphs\n## Amenability and the HRT converse\n## Improved quantitative bound in the unbiased binary setting\n## Information skeleton and information measures\n## Key entropy estimate and coupling idea","[{\"question\":\"What kind of local coordination problem is analyzed in the paper?\",\"answer\":\"The paper studies pure coordination games on finite graphs where each vertex selects one of two symmetric actions using only local information, and the cost is the average disagreement across edges.\"},{\"question\":\"What is the main improvement over earlier amenability bounds?\",\"answer\":\"In the unbiased binary setting, the paper replaces the earlier square-root loss with an entropy-based loss, proving an amenability parameter of order εlog(1/ε) when the average binary disagreement is at most ε.\"},{\"question\":\"How does the paper use information measures to obtain the improved bound?\",\"answer\":\"It assigns to each player’s local output a probability measure derived from mutual information revealed by an ordered list of independent information sources, then bounds the distance between such measures for agreeing players using binary 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kind of local coordination problem is analyzed in the paper?","Question",{"text":75,"@type":76},"The paper studies pure coordination games on finite graphs where each vertex selects one of two symmetric actions using only local information, and the cost is the average disagreement across edges.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main improvement over earlier amenability bounds?",{"text":80,"@type":76},"In the unbiased binary setting, the paper replaces the earlier square-root loss with an entropy-based loss, proving an amenability parameter of order εlog(1/ε) when the average binary disagreement is at most ε.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper use information measures to obtain the improved bound?",{"text":84,"@type":76},"It assigns to each player’s local output a probability measure derived from mutual information revealed by an ordered list of independent information sources, then bounds the distance between such measures 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