[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81936-en":3,"doc-seo-81936-105":31,"detail-sidebar-cat-0-en-105":93},{"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":28,"seo_description":14,"update_tm":29,"read_time":30},81936,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Dynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks","The paper studies coevolutionary opinion formation games on dynamic social networks under stochastic topology changes, focusing on the K-NN Markov game where network edges evolve via time-varying randomized neighbor selection. It analyzes general-sum Markov game convergence using multi-agent reinforcement learning and online learning methods, addressing extra positive Q-value terms in optimistic gradient ascent regret. Results establish weaker convergence to approximate Nash equilibria and related bounds, extending beyond correlated equilibria.","arXiv :2607 .05580v2 [ cs .GT] 10 Jul 2026  \nDynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks  \nPo-An Chen 1 , Chi-Jen Lu2 , Chuang-Chieh Lin3 , Jim Shi4 , and Chih-Chieh Hung5  \n1 Institute of Information Management, National Yang Ming Chiao Tung University, Taiwan  \n[poanchen@nycu.edu.tw](poanchen@nycu.edu.tw)  \n2 Institute of Information Science, Academia Sinica, Taiwan  \n[cjlu@iis.sinica.edu.tw](cjlu@iis.sinica.edu.tw)  \n3 Department of Computer Science and Engineering, National Taiwan Ocean University, Taiwan  \n[josephcclin@mail.ntou.edu.tw](josephcclin@mail.ntou.edu.tw)  \n4 Tuchman School of Management, New Jersey Institute of Technology, USA  \n[jshi@njit.edu](jshi@njit.edu)  \n5 Department of Management Information and Information Systems, National Chung Hsin University, Taiwan  \n[smalloshin@nchu.edu.tw](smalloshin@nchu.edu.tw)  \nAbstract. While deterministic variants of the coevolutionary opinion formation games such as the KNearest Neighbor (K-NN) game ([5]) in a dynamic social network environment can sometimes be shown to stabilize using potential functions or localized smoothness arguments, introducing stochasticity fundamentally changes the mathematical landscape. In the “K-NN Markov game\", network topologies evolve via a time-varying, randomized selection process. Proving whether such a system, as a special case of general-sum Markov games, converges to an equilibrium is a profoundly non-obvious and challenging theoretical question.  \nMultiagent reinforcement learning has been shown to derive Nash (minimax) equilibria in two-player zero-sum Markov games and Markov potential games (along with some price-of-anarchy types of results) . In recent work, optimistic dynamics are shown to converge to correlated equilibria in generalsum Markov games while the price-of-anarchy bounds are unknown. We thus analyze playing specific no-regret algorithms in general-sum Markov games for convergence to a stricter set than correlated equilibria.  \nWe integrate the convergence analysis techniques from multi-agent reinforcement learning in works of Wei et al. and online learning in a recent work of Anagnostides et al.. Specifically in (generalsum) Markov games, since the regret of the optimistic gradient ascent algorithm would have extra positive terms coming from Q-values, taking care of these terms requires non-trivial extra work setting an appropriate range of our learning rate and deriving the threshold on the number of iterations for convergence or a bounded price of anarchy, significantly different from those in the assumption in a main technical theorem of Anagnostides et al.. We analyze a weaker sense of convergences to approximate Nash equilibria by playing optimistic gradient ascents in general-sum Markov games. Specific no-regret algorithms beyond zero-sum Markov games converge not only to correlated equilibria, but also to approximate Nash equilibria (a stricter set than correlated equilibria) or a bounded price of anarchy.  \nKeywords: Markov Coevolutionary Opinion Games, Optimistic Gradient Ascent, Approximate Nash Equilibria.  \n1 Introduction  \nIn classical models of social networks, opinion dynamics and network topology are frequently analyzed in isolation [11,12][6,5,9] . Either opinions change over a fixed graph structure, or the network adapts based on static attributes of the nodes. However, real-world social environments exhibit a coevolutionary feedback loop: individuals adjust their expressed opinions to better align with their friends, while simultaneously rewriting their social ties to gravitate toward those with compatible views [5] . When formalized as a game, this interaction yields a complex, dual-layered dynamical system where continuous actions (expressed opinions) shape discrete states (network topologies), which in turn dictate the payoffs that drive subsequent actions.  \nWhile deterministic variants of these coevolutionary games such as the K-Neares","cbCair2PlMXhJ7aK","https://ap.wps.com/l/cbCair2PlMXhJ7aK","pdf",530994,5,1,15,"English","en",105,"# Abstract\n# Introduction\n## Coevolutionary feedback in social networks\n## Stochastic effects in K-NN Markov games","[{\"question\":\"What is the K-NN Markov game in the paper?\",\"answer\":\"It is a coevolutionary opinion formation game where network topologies evolve through a time-varying randomized selection process rather than deterministic closest-neighbor connections.\"},{\"question\":\"Why does adding stochasticity make equilibrium convergence difficult?\",\"answer\":\"Random neighbor selection continuously allows suboptimal links with non-zero probability, which can repeatedly disrupt local consensus and lead to challenging coupled dynamics across the network.\"},{\"question\":\"What convergence concept does the paper mainly establish?\",\"answer\":\"It studies optimistic no-regret algorithms in general-sum Markov games and analyzes weaker convergence to approximate Nash equilibria, which is stricter than correlated equilibria.\"}]","Dynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks | 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is the K-NN Markov game in the paper?","Question",{"text":77,"@type":78},"It is a coevolutionary opinion formation game where network topologies evolve through a time-varying randomized selection process rather than deterministic closest-neighbor connections.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Why does adding stochasticity make equilibrium convergence difficult?",{"text":82,"@type":78},"Random neighbor selection continuously allows suboptimal links with non-zero probability, which can repeatedly disrupt local consensus and lead to challenging coupled dynamics across the network.",{"name":84,"@type":75,"acceptedAnswer":85},"What convergence concept does the paper mainly establish?",{"text":86,"@type":78},"It studies optimistic no-regret algorithms in general-sum Markov games and analyzes weaker convergence to approximate Nash equilibria, which is stricter than correlated 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