{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T17:01:34Z","timestamp":1762102894881,"version":"3.40.3"},"publisher-location":"Cham","reference-count":40,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031263682"},{"type":"electronic","value":"9783031263699"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-26369-9_8","type":"book-chapter","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T12:43:17Z","timestamp":1675860197000},"page":"149-167","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiple Oracle Algorithm to\u00a0Solve Continuous Games"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1531-2990","authenticated-orcid":false,"given":"Tom\u00e1\u0161","family":"Kroupa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6781-5560","authenticated-orcid":false,"given":"Tom\u00e1\u0161","family":"Votroubek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"8_CR1","doi-asserted-by":"crossref","unstructured":"Adam, L., Hor\u010d\u00edk, R., Kasl, T., Kroupa, T.: Double oracle algorithm for computing equilibria in continuous games. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 5070\u20135077 (2021)","DOI":"10.1609\/aaai.v35i6.16641"},{"key":"8_CR2","volume-title":"Dynamic Noncooperative Game Theory","author":"T Ba\u015far","year":"1999","unstructured":"Ba\u015far, T., Olsder, G.: Dynamic Noncooperative Game Theory, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (1999)","edition":"2"},{"key":"8_CR3","doi-asserted-by":"crossref","unstructured":"Behnezhad, S., Blum, A., Derakhshan, M., Hajiaghayi, M., Papadimitriou, C.H., Seddighin, S.: Optimal strategies of blotto games: beyond convexity. In: Proceedings of the 2019 ACM Conference on Economics and Computation, EC 2019, ACM, New York, pp. 597\u2013616 (2019)","DOI":"10.1145\/3328526.3329608"},{"key":"8_CR4","volume-title":"Nonlinear Programming","author":"D Bertsekas","year":"2016","unstructured":"Bertsekas, D.: Nonlinear Programming. Athena Scientific, Nashua (2016)"},{"key":"8_CR5","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1613\/jair.4477","volume":"51","author":"B Bo\u0161ansk\u00fd","year":"2014","unstructured":"Bo\u0161ansk\u00fd, B., Kiekintveld, C., Lis\u00fd, V., P\u011bchou\u010dek, M.: An exact double-oracle algorithm for zero-sum extensive-form games with imperfect information. J. Artif. Intell. Res. 51, 829\u2013866 (2014)","journal-title":"J. Artif. Intell. Res."},{"issue":"2","key":"8_CR6","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1287\/moor.2015.0745","volume":"41","author":"Y Cai","year":"2016","unstructured":"Cai, Y., Candogan, O., Daskalakis, C., Papadimitriou, C.: Zero-sum polymatrix games: a generalization of minmax. Math. Oper. Res. 41(2), 648\u2013655 (2016)","journal-title":"Math. Oper. Res."},{"key":"8_CR7","unstructured":"Chasnov, B., Ratliff, L., Mazumdar, E., Burden, S.: Convergence analysis of gradient-based learning in continuous games. In: Uncertainty in Artificial Intelligence, pp. 935\u2013944. PMLR (2020)"},{"issue":"1","key":"8_CR8","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1137\/070699652","volume":"39","author":"C Daskalakis","year":"2009","unstructured":"Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1), 195\u2013259 (2009)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"8_CR9","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1137\/15M1020575","volume":"59","author":"I Dunning","year":"2017","unstructured":"Dunning, I., Huchette, J., Lubin, M.: JuMP: a modeling language for mathematical optimization. SIAM Rev. 59(2), 295\u2013320 (2017). https:\/\/doi.org\/10.1137\/15M1020575","journal-title":"SIAM Rev."},{"issue":"2","key":"8_CR10","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/S0165-1889(98)00092-X","volume":"24","author":"MC Ferris","year":"2000","unstructured":"Ferris, M.C., Munson, T.S.: Complementarity problems in GAMS and the PATH solver. J. Econ. Dyn. Control 24(2), 165\u2013188 (2000)","journal-title":"J. Econ. Dyn. Control"},{"issue":"2","key":"8_CR11","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/0022-0531(86)90118-3","volume":"38","author":"D Fudenberg","year":"1986","unstructured":"Fudenberg, D., Levine, D.: Limit games and limit equilibria. J. Econ. Theor. 38(2), 261\u2013279 (1986)","journal-title":"J. Econ. Theor."},{"issue":"2","key":"8_CR12","doi-asserted-by":"publisher","first-page":"47","DOI":"10.3390\/g12020047","volume":"12","author":"S Ganzfried","year":"2021","unstructured":"Ganzfried, S.: Algorithm for computing approximate Nash equilibrium in continuous games with application to continuous Blotto. Games 12(2), 47 (2021)","journal-title":"Games"},{"issue":"3","key":"8_CR13","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1111\/j.1751-5823.2002.tb00178.x","volume":"70","author":"AL Gibbs","year":"2002","unstructured":"Gibbs, A.L., Su, F.E.: On choosing and bounding probability metrics. Int. Stat. Rev. 70(3), 419\u2013435 (2002)","journal-title":"Int. Stat. Rev."},{"key":"8_CR14","first-page":"170","volume":"3","author":"IL Glicksberg","year":"1952","unstructured":"Glicksberg, I.L.: A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc. 3, 170\u2013174 (1952)","journal-title":"Proc. Am. Math. Soc."},{"issue":"3\u20134","key":"8_CR15","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s11127-008-9359-x","volume":"138","author":"R Golman","year":"2009","unstructured":"Golman, R., Page, S.E.: General blotto: games of allocative strategic mismatch. Public Choice 138(3\u20134), 279\u2013299 (2009)","journal-title":"Public Choice"},{"issue":"1","key":"8_CR16","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/S0022-0531(03)00005-X","volume":"110","author":"S Govindan","year":"2003","unstructured":"Govindan, S., Wilson, R.: A global Newton method to compute Nash equilibria. J. Econ. Theor. 110(1), 65\u201386 (2003)","journal-title":"J. Econ. Theor."},{"issue":"7","key":"8_CR17","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1016\/S0165-1889(03)00108-8","volume":"28","author":"S Govindan","year":"2004","unstructured":"Govindan, S., Wilson, R.: Computing Nash equilibria by iterated polymatrix approximation. J. Econ. Dyn. Control 28(7), 1229\u20131241 (2004)","journal-title":"J. Econ. Dyn. Control"},{"key":"8_CR18","volume-title":"Optimization with PDE Constraints","author":"M Hinze","year":"2008","unstructured":"Hinze, M., Pinnau, R., Ulbrich, M., Ulbrich, S.: Optimization with PDE Constraints, vol. 23. Springer, Cham (2008)"},{"issue":"1","key":"8_CR19","doi-asserted-by":"publisher","first-page":"215","DOI":"10.3934\/dcdsb.2006.6.215","volume":"6","author":"J Hofbauer","year":"2006","unstructured":"Hofbauer, J., Sorin, S.: Best response dynamics for continuous zero-sum games. Discrete Continuous Dyn. Syst.-Ser. B 6(1), 215 (2006)","journal-title":"Discrete Continuous Dyn. Syst.-Ser. B"},{"key":"8_CR20","doi-asserted-by":"crossref","unstructured":"Kamra, N., Gupta, U., Fang, F., Liu, Y., Tambe, M.: Policy learning for continuous space security games using neural networks. In: Thirty-Second AAAI Conference on Artificial Intelligence, pp. 1103\u20131112 (2018)","DOI":"10.1609\/aaai.v32i1.11446"},{"key":"8_CR21","unstructured":"Karlin, S.: Mathematical Methods and Theory in Games, Programming and Economics, Vol. 2: The Theory of Infinite Games. Addison-Wesley Publishing Company, Boston (1959)"},{"key":"8_CR22","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-030-90370-1_3","volume-title":"Decision and Game Theory for Security","author":"T Kroupa","year":"2021","unstructured":"Kroupa, T., Vannucci, S., Votroubek, T.: Separable network games with compact strategy sets. In: Bo\u0161ansk\u00fd, B., Gonzalez, C., Rass, S., Sinha, A. (eds.) Decision and Game Theory for Security, pp. 37\u201356. Springer International Publishing, Cham (2021)"},{"issue":"1\u20132","key":"8_CR23","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/s10107-010-0353-y","volume":"131","author":"R Laraki","year":"2012","unstructured":"Laraki, R., Lasserre, J.B.: Semidefinite programming for min-max problems and games. Math. Program. 131(1\u20132), 305\u2013332 (2012)","journal-title":"Math. Program."},{"key":"8_CR24","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107447226","volume-title":"An Introduction To Polynomial And Semi-Algebraic Optimization","author":"JB Lasserre","year":"2015","unstructured":"Lasserre, J.B.: An Introduction To Polynomial And Semi-Algebraic Optimization, vol. 52. Cambridge University Press, Cambridge (2015)"},{"key":"8_CR25","doi-asserted-by":"crossref","unstructured":"Li, Z., Wellman, M.P.: Evolution strategies for approximate solution of Bayesian games. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, pp. 5531\u20135540 (2021)","DOI":"10.1609\/aaai.v35i6.16696"},{"key":"8_CR26","unstructured":"McKelvey, R.D., McLennan, A.M., Turocy, T.L.: Gambit: Software tools for game theory. Version 16.0.1 (2016)"},{"key":"8_CR27","unstructured":"McMahan, H.B., Gordon, G.J., Blum, A.: Planning in the presence of cost functions controlled by an adversary. In: Proceedings of the 20th International Conference on Machine Learning (ICML-03), pp. 536\u2013543 (2003)"},{"key":"8_CR28","unstructured":"Mertikopoulos, P., Lecouat, B., Zenati, H., Foo, C.S., Chandrasekhar, V., Piliouras, G.: Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile (2018)"},{"issue":"1","key":"8_CR29","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s10107-018-1254-8","volume":"173","author":"P Mertikopoulos","year":"2019","unstructured":"Mertikopoulos, P., Zhou, Z.: Learning in games with continuous action sets and unknown payoff functions. Math. Program. 173(1), 465\u2013507 (2019)","journal-title":"Math. Program."},{"key":"8_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/978-3-030-90370-1_13","volume-title":"Decision and Game Theory for Security","author":"L Niu","year":"2021","unstructured":"Niu, L., Sahabandu, D., Clark, A., Poovendran, R.: A game-theoretic framework for controlled islanding in the presence of adversaries. In: Bo\u0161ansk\u00fd, B., Gonzalez, C., Rass, S., Sinha, A. (eds.) GameSec 2021. LNCS, vol. 13061, pp. 231\u2013250. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90370-1_13"},{"key":"8_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-38438-8","volume-title":"An Invitation To Statistics In Wasserstein Space","author":"VM Panaretos","year":"2020","unstructured":"Panaretos, V.M., Zemel, Y.: An Invitation To Statistics In Wasserstein Space. Springer Nature, Cham (2020)"},{"key":"8_CR32","doi-asserted-by":"crossref","unstructured":"Parrilo, P.: Polynomial games and sum of squares optimization. In: 2006 45th IEEE Conference on Decision and Control, pp. 2855\u20132860 (2006)","DOI":"10.1109\/CDC.2006.377261"},{"issue":"5\u20136","key":"8_CR33","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1561\/2200000073","volume":"11","author":"G Peyr\u00e9","year":"2019","unstructured":"Peyr\u00e9, G., Cuturi, M.: Computational optimal transport: with applications to data science. Found. Trends Mach. Learn. 11(5\u20136), 355\u2013607 (2019)","journal-title":"Found. Trends Mach. Learn."},{"key":"8_CR34","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.geb.2018.04.005","volume":"110","author":"J Rehbeck","year":"2018","unstructured":"Rehbeck, J.: Note on unique Nash equilibrium in continuous games. Games Econ. Behav. 110, 216\u2013225 (2018)","journal-title":"Games Econ. Behav."},{"key":"8_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/978-3-030-90370-1_5","volume-title":"Decision and Game Theory for Security","author":"B Roussillon","year":"2021","unstructured":"Roussillon, B., Loiseau, P.: Scalable optimal classifiers for\u00a0adversarial settings under uncertainty. In: Bo\u0161ansk\u00fd, B., Gonzalez, C., Rass, S., Sinha, A. (eds.) GameSec 2021. LNCS, vol. 13061, pp. 80\u201397. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90370-1_5"},{"issue":"4","key":"8_CR36","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/s00182-008-0129-2","volume":"37","author":"ND Stein","year":"2008","unstructured":"Stein, N.D., Ozdaglar, A., Parrilo, P.A.: Separable and low-rank continuous games. Int. J. Game Theor. 37(4), 475\u2013504 (2008)","journal-title":"Int. J. Game Theor."},{"key":"8_CR37","doi-asserted-by":"publisher","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2006). https:\/\/doi.org\/10.1007\/s10107-004-0559-y. https:\/\/doi.org\/10.1007\/s10107-004-0559-y","DOI":"10.1007\/s10107-004-0559-y"},{"key":"8_CR38","unstructured":"Weisser, T., Legat, B., Coey, C., Kapelevich, L., Vielma, J.P.: Polynomial and moment optimization in Julia and JuMP. In: JuliaCon (2019). https:\/\/pretalx.com\/juliacon2019\/talk\/QZBKAU\/"},{"key":"8_CR39","unstructured":"Xu, L., Perrault, A., Fang, F., Chen, H., Tambe, M.: Robust reinforcement learning under minimax regret for green security. In: Uncertainty in Artificial Intelligence, pp. 257\u2013267. PMLR (2021)"},{"key":"8_CR40","unstructured":"Yasodharan, S., Loiseau, P.: Nonzero-sum adversarial hypothesis testing games. In: Advances in Neural Information Processing Systems, pp. 7310\u20137320 (2019)"}],"container-title":["Lecture Notes in Computer Science","Decision and Game Theory for Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-26369-9_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T13:06:54Z","timestamp":1675861614000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-26369-9_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031263682","9783031263699"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-26369-9_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"9 February 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GameSec","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Decision and Game Theory for Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"PIttsburgh, PA","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 October 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 October 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gamesec2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.gamesec-conf.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"39","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"15","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"38% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}