{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T14:47:44Z","timestamp":1774018064127,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T00:00:00Z","timestamp":1762560000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T00:00:00Z","timestamp":1762560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"JSPS under Grant-in-Aid for Scientific Research","award":["22H01508"],"award-info":[{"award-number":["22H01508"]}]},{"name":"JST under ASPIRE","award":["JPMJAP2402"],"award-info":[{"award-number":["JPMJAP2402"]}]},{"name":"JSPS under Grant-in-Aid for Scientific Research Grant","award":["23K03913"],"award-info":[{"award-number":["23K03913"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s13235-025-00686-8","type":"journal-article","created":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T08:04:24Z","timestamp":1762589064000},"page":"198-219","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Perfect Bayesian Equilibria of Two-Player Games in Resilient Multiagent Systems"],"prefix":"10.1007","volume":"16","author":[{"given":"Yurid E.","family":"Nugraha","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomohisa","family":"Hayakawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hideaki","family":"Ishii","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmet","family":"Cetinkaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quanyan","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,11,8]]},"reference":[{"issue":"1","key":"686_CR1","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/MCS.2014.2364710","volume":"35","author":"Q Zhu","year":"2015","unstructured":"Zhu Q, Basar T (2015) Game-theoretic methods for robustness, security, and resilience of cyberphysical control systems: games-in-games principle for optimal cross-layer resilient control systems. IEEE Control Syst Mag 35(1):46\u201365","journal-title":"IEEE Control Syst Mag"},{"key":"686_CR2","unstructured":"Bullo F (2019) Lectures on Network Systems. Kindle Direct Publishing"},{"key":"686_CR3","doi-asserted-by":"publisher","first-page":"3843","DOI":"10.1109\/TIFS.2021.3096121","volume":"16","author":"X Wang","year":"2021","unstructured":"Wang X, Ishii H, He J, Cheng P (2021) Dynamic privacy-aware collaborative schemes for average computation: a multi-time reporting case. IEEE Trans Inf Forensics Secur 16:3843\u20133858","journal-title":"IEEE Trans Inf Forensics Secur"},{"key":"686_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2023.105579","volume":"178","author":"M Wang","year":"2023","unstructured":"Wang M, Hu J, Xu W, Cao J (2023) Leader-following event-triggered consensus control of mass under false data injection attacks. Syst Control Lett 178:105579","journal-title":"Syst Control Lett"},{"key":"686_CR5","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/j.arcontrol.2022.01.004","volume":"53","author":"H Ishii","year":"2022","unstructured":"Ishii H, Wang Y, Feng S (2022) An overview on multi-agent consensus under adversarial attacks. Annu Rev Control 53:252\u2013272","journal-title":"Annu Rev Control"},{"issue":"2","key":"686_CR6","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1109\/COMST.2022.3159185","volume":"24","author":"H Pirayesh","year":"2022","unstructured":"Pirayesh H, Zeng H (2022) Jamming attacks and anti-jamming strategies in wireless networks: a comprehensive survey. IEEE Commun Surv Tutorials 24(2):767\u2013809","journal-title":"IEEE Commun Surv Tutorials"},{"key":"686_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.108960","volume":"117","author":"A Cetinkaya","year":"2020","unstructured":"Cetinkaya A, Kikuchi K, Hayakawa T, Ishii H (2020) Randomized transmission protocols for protection against jamming attacks in multi-agent consensus. Automatica 117:108960","journal-title":"Automatica"},{"key":"686_CR8","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1109\/TCNS.2016.2549640","volume":"4","author":"Y Li","year":"2017","unstructured":"Li Y, Quevedo DE, Dey S, Shi L (2017) SINR-based DoS attack on remote state estimation: a game-theoretic approach. IEEE Trans Control Netw Syst 4:632\u2013642","journal-title":"IEEE Trans Control Netw Syst"},{"issue":"7","key":"686_CR9","doi-asserted-by":"publisher","first-page":"6063","DOI":"10.1109\/TVT.2018.2810865","volume":"67","author":"Q Wang","year":"2018","unstructured":"Wang Q, Nguyen T, Pham K, Kwon H (2018) Mitigating jamming attack: a game-theoretic perspective. IEEE Trans Veh Technol 67(7):6063\u20136074","journal-title":"IEEE Trans Veh Technol"},{"issue":"10","key":"686_CR10","doi-asserted-by":"publisher","first-page":"9793","DOI":"10.1109\/JIOT.2020.2982613","volume":"7","author":"A Signori","year":"2020","unstructured":"Signori A, Chiariotti F, Campagnaro F, Zorzi M (2020) A game-theoretic and experimental analysis of energy-depleting underwater jamming attacks. IEEE Internet Things J 7(10):9793\u20139804","journal-title":"IEEE Internet Things J"},{"key":"686_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejcon.2022.100693","volume":"68","author":"Y Nugraha","year":"2022","unstructured":"Nugraha Y, Cetinkaya A, Hayakawa T, Ishii H, Zhu Q (2022) Rolling horizon games of resilient networks with non-uniform horizons. Eur J Control 68:100693","journal-title":"Eur J Control"},{"issue":"1","key":"686_CR12","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1109\/TCNS.2020.3016839","volume":"8","author":"Y Nugraha","year":"2021","unstructured":"Nugraha Y, Cetinkaya A, Hayakawa T, Ishii H, Zhu Q (2021) Dynamic resilient network games with applications to multiagent consensus. IEEE Trans Control Netw Syst 8(1):246\u2013259","journal-title":"IEEE Trans Control Netw Syst"},{"key":"686_CR13","doi-asserted-by":"publisher","first-page":"179","DOI":"10.2307\/1885060","volume":"102","author":"I Cho","year":"1987","unstructured":"Cho I, Kreps DM (1987) Signaling games and stable equilibria. Q J Econ 102:179\u2013222","journal-title":"Q J Econ"},{"key":"686_CR14","unstructured":"Osborne MJ (2004) An introduction to game theory. Oxford University Press"},{"issue":"1","key":"686_CR15","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1109\/TAC.2018.2809863","volume":"64","author":"D Vasal","year":"2019","unstructured":"Vasal D, Sinha A, Anastasopoulos A (2019) A systematic process for evaluating structured Perfect Bayesian equilibria in dynamic games with asymmetric information. IEEE Trans Autom Control 64(1):81\u201396","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"686_CR16","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1109\/TAC.2016.2544936","volume":"62","author":"Y Ouyang","year":"2017","unstructured":"Ouyang Y, Tavafoghi H, Teneketzis D (2017) Dynamic games with asymmetric information: Common information based perfect Bayesian equilibria and sequential decomposition. IEEE Trans Autom Control 62(1):222\u2013237","journal-title":"IEEE Trans Autom Control"},{"key":"686_CR17","doi-asserted-by":"crossref","unstructured":"Castiglioni M, Celli A, Marchesi A, Gatti N (2021) Signaling in Bayesian network congestion games: the subtle power of symmetry. In: Proc. AAAI Conference on Artificial Intelligence, pp. 5252\u20135259","DOI":"10.1609\/aaai.v35i6.16663"},{"issue":"9","key":"686_CR18","doi-asserted-by":"publisher","first-page":"2250","DOI":"10.1109\/TSP.2014.2309073","volume":"62","author":"C Eksin","year":"2014","unstructured":"Eksin C, Molavi P, Ribeiro A, Jadbabaie A (2014) Bayesian quadratic network game filters. IEEE Trans Signal Process 62(9):2250\u20132264","journal-title":"IEEE Trans Signal Process"},{"issue":"3","key":"686_CR19","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.1109\/TAC.2018.2833140","volume":"64","author":"D Gadjov","year":"2019","unstructured":"Gadjov D, Pavel L (2019) A passivity-based approach to Nash equilibrium seeking over networks. IEEE Trans Autom Control 64(3):1077\u20131092","journal-title":"IEEE Trans Autom Control"},{"issue":"11","key":"686_CR20","doi-asserted-by":"publisher","first-page":"5793","DOI":"10.1109\/TAC.2021.3122372","volume":"67","author":"Y Wu","year":"2022","unstructured":"Wu Y, Le S, Zhang K, Sun X-M (2022) Agent transformation of Bayesian games. IEEE Trans Autom Control 67(11):5793\u20135808","journal-title":"IEEE Trans Autom Control"},{"issue":"8","key":"686_CR21","first-page":"3400","volume":"69","author":"Y Li","year":"2022","unstructured":"Li Y, Zhu Y, Li T, Zheng B-C (2022) Distributed Nash equilibrium seeking in a multi-coalition noncooperative game under incomplete decision information. IEEE Trans Circuits Syst II Express Briefs 69(8):3400\u20133404","journal-title":"IEEE Trans Circuits Syst II Express Briefs"},{"issue":"2","key":"686_CR22","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1109\/TCNS.2021.3124170","volume":"9","author":"D Cappello","year":"2022","unstructured":"Cappello D, Mylvaganam T (2022) Distributed differential games for control of multi-agent systems. IEEE Trans Control Netw Syst 9(2):635\u2013646","journal-title":"IEEE Trans Control Netw Syst"},{"issue":"1","key":"686_CR23","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1109\/TPWRS.2004.831269","volume":"20","author":"PF Correia","year":"2005","unstructured":"Correia PF (2005) Games with incomplete and asymmetric information in Poolco markets. IEEE Trans Power Syst 20(1):83\u201389","journal-title":"IEEE Trans Power Syst"},{"key":"686_CR24","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1109\/TICPS.2024.3396106","volume":"2","author":"Y Li","year":"2024","unstructured":"Li Y, Liu S, Zhu L (2024) A stochastic Bayesian game for securing secondary frequency control of microgrids against spoofing attacks with incomplete information. IEEE Trans Indus Cyber Phys Syst 2:118\u2013129","journal-title":"IEEE Trans Indus Cyber Phys Syst"},{"issue":"10","key":"686_CR25","doi-asserted-by":"publisher","first-page":"1991","DOI":"10.1109\/LCOMM.2016.2598808","volume":"20","author":"L Jia","year":"2016","unstructured":"Jia L, Yao F, Sun Y, Niu Y, Zhu Y (2016) Bayesian Stackelberg game for antijamming transmission with incomplete information. IEEE Commun Lett 20(10):1991\u20131994","journal-title":"IEEE Commun Lett"},{"key":"686_CR26","first-page":"527","volume":"10","author":"Y Wang","year":"2024","unstructured":"Wang Y, Xing W, Zhang J, Liu L, Zhao X (2024) Remote state estimation under DoS attacks in CPSs with arbitrary tree topology: a Bayesian Stackelberg game approach. IEEE Trans Signal Inf Process Over Netw 10:527\u2013538","journal-title":"IEEE Trans Signal Inf Process Over Netw"},{"issue":"12","key":"686_CR27","first-page":"4894","volume":"71","author":"H He","year":"2024","unstructured":"He H, Duan H, Yuan W, Zeng Z (2024) A potential game approach to target assignment in heterogeneous manned\/unmanned aerial team with incomplete information. IEEE Trans Circuits Syst II Express Briefs 71(12):4894\u20134898","journal-title":"IEEE Trans Circuits Syst II Express Briefs"},{"issue":"3","key":"686_CR28","doi-asserted-by":"publisher","first-page":"4626","DOI":"10.1109\/TTE.2023.3237929","volume":"9","author":"Y Liu","year":"2023","unstructured":"Liu Y, Zong C, Dai C, Zheng H, Zhang D (2023) Behavioral decision-making approach for vehicle platoon control: Two noncooperative game models. IEEE Trans Transp Electrific 9(3):4626\u20134638","journal-title":"IEEE Trans Transp Electrific"},{"key":"686_CR29","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1109\/LCSYS.2021.3087097","volume":"6","author":"H Sasahara","year":"2021","unstructured":"Sasahara H, Sandberg H (2021) Epistemic signaling games for cyber deception with asymmetric recognition. IEEE Control Syst Lett 6:854\u2013859","journal-title":"IEEE Control Syst Lett"},{"key":"686_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2020.108883","volume":"115","author":"S Sar\u0131ta\u015f","year":"2020","unstructured":"Sar\u0131ta\u015f S, Y\u00fcksel S, Gezici S (2020) Dynamic signaling games with quadratic criteria under Nash and Stackelberg equilibria. Automatica 115:108883","journal-title":"Automatica"},{"key":"686_CR31","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/j.geb.2007.10.010","volume":"64","author":"D K\u00fcbler","year":"2008","unstructured":"K\u00fcbler D, M\u00fcller W, Normann H-T (2008) Job-market signaling and screening: an experimental comparison. Games Econom Behav 64:219\u2013236","journal-title":"Games Econom Behav"},{"key":"686_CR32","doi-asserted-by":"crossref","unstructured":"Stiglitz J, Weiss A (1990) Sorting out the differences between signaling and screening models. NBER Technical Working Papers, 0093","DOI":"10.3386\/t0093"},{"issue":"4","key":"686_CR33","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1257\/jep.30.4.151","volume":"30","author":"D Fudenberg","year":"2016","unstructured":"Fudenberg D, Levine DK (2016) Whither game theory? Towards a theory of learning in games. J Econ Perspect 30(4):151\u201370","journal-title":"J Econ Perspect"},{"issue":"11","key":"686_CR34","doi-asserted-by":"publisher","first-page":"4512","DOI":"10.1109\/TNNLS.2019.2955857","volume":"31","author":"S Paul","year":"2020","unstructured":"Paul S, Ni Z, Mu C (2020) A learning-based solution for an adversarial repeated game in cyber-physical power systems. IEEE Trans Neural Netw Learn Syst 31(11):4512\u20134523","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"7","key":"686_CR35","doi-asserted-by":"publisher","first-page":"7174","DOI":"10.1109\/TVT.2019.2914032","volume":"68","author":"Y Yuan","year":"2019","unstructured":"Yuan Y, Yang T, Feng H, Hu B (2019) Learning for matching game in cooperative D2D communication with incomplete information. IEEE Trans Veh Technol 68(7):7174\u20137178","journal-title":"IEEE Trans Veh Technol"},{"key":"686_CR36","unstructured":"Condorelli D, Furlan M (2024) Deep learning across games. arXiv preprint, arXiv:2409.15197 [econ.TH]"},{"key":"686_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109846","volume":"133","author":"S Krila\u0161evi\u0107","year":"2021","unstructured":"Krila\u0161evi\u0107 S, Grammatico S (2021) Learning generalized Nash equilibria in multi-agent dynamical systems via extremum seeking control. Automatica 133:109846","journal-title":"Automatica"},{"key":"686_CR38","doi-asserted-by":"crossref","unstructured":"Nugraha YE, Hayakawa T, Ishii H, Cetinkaya A, Zhu Q (2023) Two-player incomplete games of resilient multiagent systems. In: Proc. 22nd IFAC World Congress, vol. 56, pp. 258\u2013263","DOI":"10.1016\/j.ifacol.2023.10.1578"},{"key":"686_CR39","doi-asserted-by":"publisher","first-page":"2434","DOI":"10.1109\/TAC.2016.2612818","volume":"62","author":"A Cetinkaya","year":"2017","unstructured":"Cetinkaya A, Ishii H, Hayakawa T (2017) Networked control under random and malicious packet losses. IEEE Trans Autom Control 62:2434\u20132449","journal-title":"IEEE Trans Autom Control"},{"key":"686_CR40","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1109\/TCNS.2017.2668901","volume":"5","author":"D Senejohnny","year":"2018","unstructured":"Senejohnny D, Tesi P, De Persis C (2018) A jamming resilient algorithm for self-triggered network coordination. IEEE Trans Control Netw Syst 5:981\u2013990","journal-title":"IEEE Trans Control Netw Syst"},{"key":"686_CR41","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.geb.2019.11.011","volume":"120","author":"D Fudenberg","year":"2020","unstructured":"Fudenberg D, He K (2020) Payoff information and learning in signaling games. Games Econom Behav 120:96\u2013120","journal-title":"Games Econom Behav"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-025-00686-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13235-025-00686-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-025-00686-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T13:02:41Z","timestamp":1774011761000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13235-025-00686-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,8]]},"references-count":41,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["686"],"URL":"https:\/\/doi.org\/10.1007\/s13235-025-00686-8","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"value":"2153-0785","type":"print"},{"value":"2153-0793","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,8]]},"assertion":[{"value":"29 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}