[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85142-en":3,"doc-seo-85142-105":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},85142,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Eigenmanifold in Game: Evidence from Human Continuous Strategy Game Experiments","Evolutionary game dynamics contains a hypothesis that the steady-state dynamic structure is described by a linear superposition of eigenmanifolds. The eigenmanifold composition depends on eigenvector structure at the Nash equilibrium and is governed by the game’s evolutionary dynamics equations. Prior evidence mainly concerns discrete-strategy games. Using human-subject experimental data in continuous-strategy games, this work finds significant support for the hypothesis, extending manifold-based representation and testability beyond discrete settings.","arXiv :2607 .09782v 1 [ cs .GT] 8 Jul 2026  \nEigenmanifold in Game: Evidence from human continuous  \nstrategy game experiments ∗  \nWang Zhijian, Yao Qinmei, Shan Lixia, Wang Yijia, Zhang Chuchen Experimental Social Science Laboratory, Zhejiang University, China  \nJuly 14, 2026  \nContents  \n1 Introduction 2  \n1.1 Research question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \n1.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2  \n1.3 Approach .......................................... 3  \n1.3.1 Step 0: Select Existed Experimental Game as Sample ............. 3  \n1.3.2 Step 1: Discretization ............................... 3  \n1.3.3 Step 2: Constructure Manifold Vector ...................... 4  \n1.3.4 Step 3: Statistical Test Method .......................... 5  \n1.4 Summary .......................................... 5  \n2 Results 5  \n2.1 Interpretation of Statistical Test Results ......................... 6  \n2.1.1 1. Linear Dependence between Theoretical and Experimental Manifold .... 6  \n2.1.2 2. Dominant Role of the Principal manifold ................... 7  \n2.1.3 3. Contribution of the Secondary Eigenmanifold ................ 7  \n2.2 Advantages of the Eigenmanifold Method ........................ 8  \n2.2.1 Experiment Results Presentation with Manifold ................ 9  \n2.2.2 Theoretical Prediction Presentation with Manifold . . . . . . . . . . . . . . . 9  \n2.2.3 Velocity as Projection of Manifold ........................ 10  \n2.2.4 Discussion: Two Argument ............................ 11  \n3 Appendix Method 12  \n3. 1 Definition of Theoretical Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n3.1.1 Prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n3.1.2 Defining the Eigenmanifold Vector and Its Component Eigen-Circle Scalars . 12  \n3.2 Measurement of Experimental Manifold Vector ..................... 14  \n3.2. 1 Basic Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14  \n3.2.2 Experimental Subspace Angular Momentum ¯¯Lmn . . . . . . . . . . . . . . . 15  \n3.3 Table of the Statistical Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 15  \n3.4 Table of the Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15  \n∗We thank Daniel Friedman for his helpful comments, especially for his supporting on our criticism on the “First a hammer east, then a stick west” current condition of the research field in experimental investigations of evolutionary  \ngame theory. Corresponding author: [wangzj@zju.edu.cn](wangzj@zju.edu.cn)  \nAbstract  \nIn evolutionary game dynamics, there exists a hypothesis, which states that, the dynamic structure of the game’s steady-state system is characterized by the linear superposition of eigenmanifolds, which depends specifically on the eigenvector structure at the Nash equilibrium and is ultimately governed by the evolutionary game dynamics equations. This hypotheses has been supported widely in discrete strategy game. In continuous‑strategy game, using experimental data from human‑subject games, this paper finds that the hypothesis is supported in significant, too.  \n1 Introduction  \n1.1 Research question  \nIn game theory, the question that needs to be answered after Nash equilibrium is: how does the game move? [1, 2 , 3] The following is an analogy. When introducing a new substance, the first question a natural scientist needs to answer is its composition; after answering the composition of the new substance, the next question to be answered is its molecular structure. Faced with a new game, the first question a social scientist needs to answer is where its (Nash) equilibrium lies in the strategy space. Similarly, after understanding the equilibrium of the game, the next question to be answered is its movement structure. For example, the social cycle in rock-paper-scissors [4, 5 , 6 , ","cbCaitxdBAe1zTsh","https://ap.wps.com/l/cbCaitxdBAe1zTsh","pdf",706775,3,1,24,"English","en",105,"# Introduction\n## Research question\n## Data\n## Approach\n# Results\n## Interpretation of Statistical Test Results\n## Advantages of the Eigenmanifold Method\n# Appendix Method","[{\"question\":\"What core hypothesis about game dynamics does the paper test?\",\"answer\":\"The paper tests the hypothesis that the steady-state dynamic structure can be represented as a linear superposition of eigenmanifolds, determined by eigenvector structure at the Nash equilibrium and governed by evolutionary game dynamics equations.\"},{\"question\":\"How does the paper obtain evidence for continuous-strategy games?\",\"answer\":\"It uses experimental data from human continuous-strategy games and applies a discretization and eigenmanifold construction workflow, followed by statistical test methods to evaluate the hypothesis.\"},{\"question\":\"What are the main takeaways from the results section?\",\"answer\":\"The paper reports statistical support for the eigenmanifold hypothesis in continuous-strategy settings, including interpretations based on linear dependence between theoretical and experimental manifolds and the relative contributions of principal and secondary eigenmanifolds.\"}]",1784201337,60,{"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},"eigenmanifold-in-game-evidence-from-human-continuous-strategy-game-experiments","",{"@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/eigenmanifold-in-game-evidence-from-human-continuous-strategy-game-experiments/85142/",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","2026-07-22","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 core hypothesis about game dynamics does the paper test?","Question",{"text":75,"@type":76},"The paper tests the hypothesis that the steady-state dynamic structure can be represented as a linear superposition of eigenmanifolds, determined by eigenvector structure at the Nash equilibrium and governed by evolutionary game dynamics equations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper obtain evidence for continuous-strategy games?",{"text":80,"@type":76},"It uses experimental data from human continuous-strategy games and applies a discretization and eigenmanifold construction workflow, followed by statistical test methods to evaluate the hypothesis.",{"name":82,"@type":73,"acceptedAnswer":83},"What are the main takeaways from the results section?",{"text":84,"@type":76},"The paper reports statistical support for the eigenmanifold hypothesis in continuous-strategy settings, including interpretations based on linear dependence between theoretical and experimental manifolds and the relative contributions of principal and secondary eigenmanifolds.","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},[93,97,101,105,109,114,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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