[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85475-en":3,"doc-seo-85475-105":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},85475,962075006959,"Anda","https://ap-avatar.wpscdn.com/avatar/e0002397efbe92a78e?_k=1776741047341049297",8,"Research & Report","The Theory of Strategic Evolution: Games with Endogenous Players and Strategic Replicators","Von Neumann’s parallel work on game theory and self-reproducing automata never fully merged, leaving a gap between strategic control and replication. Rational agents optimize, yet their replication is not controlled; replicators reproduce without strategic choice. The paper develops a unified framework for strategic replicators under resource constraints, organizing results as Seven Laws that characterize dynamics, equilibria, stability, and fundamental limits. Applications connect AI deployment behavior and institutional design to constitutional constraints on stable alignment.","arXiv :2512 .0790 1v 3 [ cs .GT] 11 Jul 2026  \nThe Theory of Strategic Evolution  \nGames with Endogenous Players and the Seven Laws of Strategic  \nReplicators  \nKevin Vallier  \nInstitute of American Constitutional Thought and Leadership University of Toledo  \n[kevinvallier@gmail.com](kevinvallier@gmail.com)  \nDecember 2025 (v3.8)  \nAbstract  \nVon Neumann founded both game theory and the theory of self-reproducing automata, but the two programs never merged. Rational players do not control their replication, and replicators do not choose strategically. Contemporary AI systems expose this gap: they optimize objectives, yet the population of AI systems is not fixed but expands and contracts based on performance. When capital can spawn capital, we need a theory that captures both rationality and replication. This paper provides one.  \nThe Theory of Strategic Evolution analyzes strategic replicators: entities that optimize under resource constraints and spawn copies of themselves. The framework is organized around Seven Laws that characterize the dynamics, equilibria, stability conditions, and fundamental limits of such systems:  \n1. Strategic Selection: Mean fitness serves as a Lyapunov function; dominated types are eliminated.  \n2. ESDI Characterization: Equilibria exist, are generically finite, and satisfy Nash-KKT-LP equivalence.  \n3. H-γ Stability: Multi-level systems are stable iff the spectral radius ρ(Γ) \u003C 1.  \n4. G∞ Closure: A unique maximal class of safe modifications exists and is closed under composition.  \n5. Constitutional Duality: Shadow prices implement any frontier allocation; welfare theorems hold.  \n6. Alignment Impossibility: Full reachability destroys Lyapunov structure; alignment requires bounded modification.  \n7. Hopf Transition: At γ = 1, systems undergo supercritical bifurcation producing limit cycles.  \nApplications range from AI deployment dynamics to institutional design. The framework shows why “personality engineering” fails under selection pressure and identifies constitutional constraints necessary for stable alignment.  \nFormal verification. All seven laws are machine-verified in Lean 4 with Mathlib: 73 theorems, cold-compiling from a clean checkout with zero custom axioms (every headline depends only on propext, Classical. choice, and Quot. sound; one requires no axioms at all) . No sorry, admit, native decide, or custom axiom occurs on the load-bearing path. Source, a theorem-by-theorem contract, per-law status, and a reproducible axiom audit: [https://github. com/selfreferencing/TSE_Formal](https://github. com/selfreferencing/TSE_Formal. See)[. See](https://github. com/selfreferencing/TSE_Formal. See) Section 29.  \nKeywords: strategic evolution, game theory, self-replication, evolutionary dynamics, AI governance, constitutional political economy, impossibility theorems, Lyapunov stability JEL Codes: C73 (Stochastic and Dynamic Games; Evolutionary Games), D43 (Market Structure), O33 (Technological Change), P16 (Political Economy) ArXiv Categories: cs.GT (Primary); cs.AI, econ.TH (Cross-list) MSC Codes: 91A22 (Evolutionary games), 91A80 (Applications of game theory), 91B55 (Economic dynamics)  \nContents  \nI Foundations 10  \n1 Introduction 10  \n1.1 Strategic Replicators ............................... 10  \n1.2 The Von Neumann Synthesis ........................... 11  \n1.3 Main Contributions ................................ 11  \n1.4 The Seven Laws: An Overview ......................... 12  \n1.4.1 Connections Among the Laws ...................... 14  \n1.5 Relation to Existing Literature ......................... 14  \n1.5.1 Von Neumann’s Three Programs .................... 14  \n1.5.2 Evolutionary Game Theory ....................... 15  \n1.5.3 Multi-Agent Reinforcement Learning and Mean-Field Games ..... 16  \n1.5.4 Mechanism Design ............................ 17  \n1.5.5 Constitutional Political Economy .................... 18  \n1.5.6 AI Safety and Alignment ......................... 18  \n1.5.7 Why Exi","cbCaiurZmIgGyFcM","https://ap.wps.com/l/cbCaiurZmIgGyFcM","pdf",909121,3,1,169,"English","en",105,"# Foundations\n## Introduction\n## Strategic Replicators\n## The Von Neumann Synthesis\n## Main Contributions\n## The Seven Laws: An Overview\n## Relation to Existing Literature\n# The Seven Laws of Strategic Evolution\n## Law 1: Strategic Selection\n## ESDI Characterization\n## Strategic-Replicator Class Hierarchy","[{\"question\":\"What problem does the paper address about game theory and replication?\",\"answer\":\"It addresses the mismatch where rational players do not control their replication and replicators do not behave strategically. Contemporary AI highlights this gap because the population of systems expands or contracts with performance, not as a fixed set of agents.\"},{\"question\":\"What are “strategic replicators” in the paper’s framework?\",\"answer\":\"Strategic replicators are entities that optimize under resource constraints and spawn copies of themselves. The framework analyzes how such entities produce dynamics, equilibria, stability conditions, and limits for these systems.\"},{\"question\":\"How do the Seven Laws relate to stability and alignment?\",\"answer\":\"The laws provide conditions for dynamics and equilibria, including a stability criterion based on spectral radius. They also show why full reachability can destroy Lyapunov structure and argue that alignment requires bounded modification, with constitutional constraints enabling stable alignment.\"}]",1784203874,426,{"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},"the-theory-of-strategic-evolution-games-with-endogenous-players-and-strategic-replicators","",{"@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/the-theory-of-strategic-evolution-games-with-endogenous-players-and-strategic-replicators/85475/",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","2026-07-24","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 problem does the paper address about game theory and replication?","Question",{"text":75,"@type":76},"It addresses the mismatch where rational players do not control their replication and replicators do not behave strategically. Contemporary AI highlights this gap because the population of systems expands or contracts with performance, not as a fixed set of agents.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What are “strategic replicators” in the paper’s framework?",{"text":80,"@type":76},"Strategic replicators are entities that optimize under resource constraints and spawn copies of themselves. The framework analyzes how such entities produce dynamics, equilibria, stability conditions, and limits for these systems.",{"name":82,"@type":73,"acceptedAnswer":83},"How do the Seven Laws relate to stability and alignment?",{"text":84,"@type":76},"The laws provide conditions for dynamics and equilibria, including a stability criterion based on spectral radius. They also show why full reachability can destroy Lyapunov structure and argue that alignment requires bounded modification, with constitutional constraints enabling stable alignment.","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"]