{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T20:32:40Z","timestamp":1726345960843},"reference-count":49,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T00:00:00Z","timestamp":1625097600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["European Journal of Operational Research"],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1016\/j.ejor.2020.10.015","type":"journal-article","created":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T17:01:25Z","timestamp":1603818085000},"page":"95-107","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":7,"title":["Counterfactual regret minimization for integrated cyber and air defense resource allocation"],"prefix":"10.1016","volume":"292","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-8583-7763","authenticated-orcid":false,"given":"Andrew","family":"Keith","sequence":"first","affiliation":[]},{"given":"Darryl","family":"Ahner","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0001","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s10107-005-0686-0","article-title":"Robust game theory","volume":"107","author":"Aghassi","year":"2006","journal-title":"Mathematical Programming"},{"issue":"8","key":"10.1016\/j.ejor.2020.10.015_bib0002","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1007\/s11590-014-0823-x","article-title":"Optimal multi-stage allocation of weapons to targets using adaptive dynamic programming","volume":"9","author":"Ahner","year":"2014","journal-title":"Optimization Letters"},{"issue":"5","key":"10.1016\/j.ejor.2020.10.015_bib0003","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1287\/opre.1110.0983","article-title":"Patrolling games","volume":"59","author":"Alpern","year":"2011","journal-title":"Operations Research"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0004","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1137\/141000671","article-title":"Julia: A fresh approach to numerical computing","volume":"59","author":"Bezanson","year":"2017","journal-title":"SIAM Review"},{"issue":"6","key":"10.1016\/j.ejor.2020.10.015_bib0005","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s10732-017-9350-0","article-title":"Heterogeneous surface-to-air missile defense battery location: A game theoretic approach","volume":"23","author":"Boardman","year":"2017","journal-title":"Journal of Heuristics"},{"key":"10.1016\/j.ejor.2020.10.015_bib0006","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1613\/jair.4477","article-title":"An exact double-oracle algorithm for zero-sum extensive-form games with imperfect information","volume":"51","author":"Bosansky","year":"2014","journal-title":"Journal of Artificial Intelligence Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0007","unstructured":"Brown, N., Lerer, A., Gross, S., & Sandholm, T. (2018). Deep counterfactual regret minimization. https:\/\/arxiv.org\/abs\/1710.11424."},{"key":"10.1016\/j.ejor.2020.10.015_bib0008","unstructured":"Brown, N., & Sandholm, T. (2018). Solving imperfect-information games via discounted regret minimization. http:\/\/arxiv.org\/abs\/1809.04040. arXiv:1809.04040v2"},{"key":"10.1016\/j.ejor.2020.10.015_bib0009","article-title":"Attacker-defender model against quantal response adversaries for cyber security in logistics management: An introductory study","author":"Cheung","year":"2019","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"10.1016\/j.ejor.2020.10.015_bib0010","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1016\/j.ejor.2016.11.023","article-title":"Approximate dynamic programming for missile defense interceptor fire control","volume":"259","author":"Davis","year":"2017","journal-title":"European Journal of Operational Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0011","unstructured":"Davis, T., Waugh, K., & Bowling, M. (2018). Solving large extensive-form games with strategy constraints. https:\/\/arxiv.org\/abs\/1809.07893arXiv:1809.07893v1"},{"key":"10.1016\/j.ejor.2020.10.015_bib0012","unstructured":"Farina, G., Kroer, C., & Sandholm, T. (2017). Regret minimization in behaviorally-constrained zero-sum games. http:\/\/arxiv.org\/abs\/1711.03441."},{"key":"10.1016\/j.ejor.2020.10.015_bib0013","series-title":"Proceedings of the International symposium on architecting critical systems","first-page":"125","article-title":"Towards net-centric cyber survivability for ballistic missile defense","author":"Gagnon","year":"2010"},{"issue":"2","key":"10.1016\/j.ejor.2020.10.015_sbref0014","doi-asserted-by":"crossref","DOI":"10.1145\/2716322","article-title":"Safe opponent exploitation","volume":"3","author":"Ganzfried","year":"2015","journal-title":"ACM Transactions on Economics and Computation"},{"key":"10.1016\/j.ejor.2020.10.015_bib0015","series-title":"Proceedings of the IEEE conference on computational intelligence and games, CIG","first-page":"1","article-title":"Bayesian opponent exploitation in imperfect-information games","author":"Ganzfried","year":"2018"},{"issue":"3","key":"10.1016\/j.ejor.2020.10.015_bib0016","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1287\/ijoc.2016.0690","article-title":"A game theoretic model for the optimal location of Integrated Air Defense System missile batteries","volume":"28","author":"Han","year":"2016","journal-title":"INFORMS Journal on Computing"},{"key":"10.1016\/j.ejor.2020.10.015_bib0017","series-title":"Proceedings of the 26th annual conference on innovative applications of artificial intelligence","first-page":"2978","article-title":"Robust protection of fisheries with COmPASS","author":"Haskell","year":"2014"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0018","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1214\/aoms\/1177703732","article-title":"Robust estimation of a location parameter","volume":"35","author":"Huber","year":"1964","journal-title":"The Annals of Mathematical Statistics"},{"key":"10.1016\/j.ejor.2020.10.015_bib0019","series-title":"Proceedings of the international conference on autonomous agents and multi-agent systems","first-page":"215","article-title":"Security scheduling for real-world networks","author":"Jain","year":"2013"},{"key":"10.1016\/j.ejor.2020.10.015_bib0020","series-title":"Proceedings of the 11th international conference on autonomous agents and multiagent systems - Volume 2","first-page":"837","article-title":"Efficient Nash equilibrium approximation through Monte Carlo counterfactual regret minimization","author":"Johanson","year":"2012"},{"key":"10.1016\/j.ejor.2020.10.015_bib0021","series-title":"Proceedings of the 12th international conference on artificial intelligence and statistics (AISTATS)","first-page":"264","article-title":"Data biased robust counter strategies","author":"Johanson","year":"2009"},{"key":"10.1016\/j.ejor.2020.10.015_bib0022","series-title":"Advances in neural information processing systems","first-page":"721","article-title":"Computing robust counter-strategies","author":"Johanson","year":"2008"},{"key":"10.1016\/j.ejor.2020.10.015_bib0023","series-title":"Handbook of dynamic game theory","article-title":"Trends and applications in stackelberg security games","author":"Kar","year":"2016"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0024","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.orl.2013.10.005","article-title":"On discounted stochastic games with incomplete information on payoffs and a security application","volume":"42","author":"Karde\u015f","year":"2014","journal-title":"Operations Research Letters"},{"issue":"3","key":"10.1016\/j.ejor.2020.10.015_bib0025","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1016\/j.ejor.2019.04.035","article-title":"Scalable min-max multi-objective cyber-security optimisation over probabilistic attack graphs","volume":"278","author":"Khouzani","year":"2019","journal-title":"European Journal of Operational Research"},{"issue":"5","key":"10.1016\/j.ejor.2020.10.015_bib0026","first-page":"90:1","article-title":"A survey on game theoretic approaches for intrusion detection and response optimization","volume":"51","author":"Kiennert","year":"2018","journal-title":"ACM Computing Surveys"},{"key":"10.1016\/j.ejor.2020.10.015_bib0027","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.cor.2018.10.015","article-title":"The weapon-target assignment problem","volume":"105","author":"Kline","year":"2018","journal-title":"Computers and Operations Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0028","first-page":"1","article-title":"Real-time heuristic algorithms for the static weapon target assignment problem","author":"Kline","year":"2017","journal-title":"Journal of Heuristics"},{"key":"10.1016\/j.ejor.2020.10.015_bib0029","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1613\/jair.3269","article-title":"Stackelberg vs. Nash in security games: An extended investigation of interchangeability, equivalence, and uniqueness","volume":"41","author":"Korzhyk","year":"2011","journal-title":"Journal of Artificial Intelligence Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0030","series-title":"Proceedings of the annual conference on neural information processing systems (NIPS)","article-title":"Solving large sequential games with the excessive gap technique","author":"Kroer","year":"2018"},{"key":"10.1016\/j.ejor.2020.10.015_bib0031","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.cor.2018.05.017","article-title":"A bilevel exposure-oriented sensor location problem for border security","volume":"98","author":"Lessin","year":"2018","journal-title":"Computers and Operations Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0032","series-title":"Proceedings of the 30th conference on artificial intelligence (AAAI-16)","first-page":"544","article-title":"Counterfactual regret minimization in sequential security games","author":"Lisy","year":"2016"},{"issue":"2","key":"10.1016\/j.ejor.2020.10.015_bib0033","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.ejor.2017.07.050","article-title":"Distributionally robust equilibrium for continuous games: Nash and Stackelberg models","volume":"265","author":"Liu","year":"2018","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0034","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1147\/rd.471.0057","article-title":"The common optimization interface for operations research","volume":"47","author":"Lougee-Heimer","year":"2003","journal-title":"IBM Journal of Research and Development"},{"issue":"10","key":"10.1016\/j.ejor.2020.10.015_bib0035","doi-asserted-by":"crossref","first-page":"2490","DOI":"10.1109\/TIFS.2018.2819967","article-title":"A POMDP approach to the dynamic defense of large-scale cyber networks","volume":"13","author":"Miehling","year":"2018","journal-title":"IEEE Transactions on Information Forensics and Security"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0036","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1137\/S1052623403422285","article-title":"Excessive gap technique in nonsmooth convex minimization","volume":"16","author":"Nesterov","year":"2005","journal-title":"SIAM Journal on Optimization"},{"key":"10.1016\/j.ejor.2020.10.015_bib0037","series-title":"Proceedings of the 13th international conference on autonomous agents and multiagent systems (AAMAS)","first-page":"317","article-title":"Stop the compartmentalization: Unified robust algorithms for handling uncertainties in security games","author":"Nguyen","year":"2014"},{"key":"10.1016\/j.ejor.2020.10.015_bib0038","series-title":"Proceedings of the IEEE international parallel and distributed processing symposium workshops (IPDPS)","first-page":"1831","article-title":"Addressing behavioral uncertainty in security games: An efficient robust strategic solution for defender patrols","author":"Nguyen","year":"2016"},{"issue":"4","key":"10.1016\/j.ejor.2020.10.015_bib0039","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1057\/s41273-017-0054-0","article-title":"Simulating attacker and defender strategies within a dynamic game on network topology","volume":"12","author":"Nystrom","year":"2018","journal-title":"Journal of Simulation"},{"key":"10.1016\/j.ejor.2020.10.015_bib0040","first-page":"575","article-title":"Computing approximate Nash equilibria and robust best-responses using sampling","volume":"42","author":"Ponsen","year":"2011","journal-title":"Journal of Artificial Intelligence Research"},{"key":"10.1016\/j.ejor.2020.10.015_bib0041","series-title":"Approximate dynamic programming: solving the curses of dimensionality","author":"Powell","year":"2007"},{"key":"10.1016\/j.ejor.2020.10.015_bib0042","series-title":"Multiagent systems: algorithmic, game-theoretic, and logical foundations","author":"Shoham","year":"2008"},{"issue":"7","key":"10.1016\/j.ejor.2020.10.015_bib0043","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.1007\/s11590-016-1077-6","article-title":"Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium","volume":"11","author":"Singh","year":"2017","journal-title":"Optimization Letters"},{"issue":"1","key":"10.1016\/j.ejor.2020.10.015_bib0044","first-page":"19","article-title":"From physical security to cybersecurity","volume":"1","author":"Sinha","year":"2015","journal-title":"Journal of Cybersecurity"},{"key":"10.1016\/j.ejor.2020.10.015_bib0045","series-title":"Proceedings of the international joint conference on artificial intelligence","first-page":"645","article-title":"Solving heads-up limit Texas hold\u2019em","author":"Tammelin","year":"2015"},{"key":"10.1016\/j.ejor.2020.10.015_bib0046","series-title":"Technical Report","article-title":"Air force future operating concept","author":"United States Air Force","year":"2015"},{"key":"10.1016\/j.ejor.2020.10.015_bib0047","series-title":"Technical Report","article-title":"Strategic master plan","author":"United States Air Force","year":"2015"},{"key":"10.1016\/j.ejor.2020.10.015_bib0048","unstructured":"United States Cyber Command (2018). Cyber mission force achieves full operational capability. https:\/\/dod.defense.gov\/News\/Article\/Article\/1524747\/cyber-mission-force-achieves-full-operational-capability\/."},{"key":"10.1016\/j.ejor.2020.10.015_bib0049","first-page":"1729","article-title":"Regret minimization in games with incomplete information","author":"Zinkevich","year":"2008","journal-title":"Advances in Neural Information Processing Systems"}],"container-title":["European Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377221720308912?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377221720308912?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T01:21:31Z","timestamp":1613697691000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377221720308912"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7]]},"references-count":49,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["S0377221720308912"],"URL":"https:\/\/doi.org\/10.1016\/j.ejor.2020.10.015","relation":{},"ISSN":["0377-2217"],"issn-type":[{"value":"0377-2217","type":"print"}],"subject":[],"published":{"date-parts":[[2021,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Counterfactual regret minimization for integrated cyber and air defense resource allocation","name":"articletitle","label":"Article Title"},{"value":"European Journal of Operational Research","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ejor.2020.10.015","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Published by Elsevier B.V.","name":"copyright","label":"Copyright"}]}}