{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:39:07Z","timestamp":1740145147658,"version":"3.37.3"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T00:00:00Z","timestamp":1719187200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T00:00:00Z","timestamp":1719187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N000142112262"],"award-info":[{"award-number":["N000142112262"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["3R01CA257814-02S1"],"award-info":[{"award-number":["3R01CA257814-02S1"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose an extension of two-player zero-sum games, where one player may select available actions for themselves and the opponent, subject to a budget constraint. We present a mixed-integer linear programming (MILP) formulation for the problem, provide analytical results regarding its solution, and discuss applications in the security and advertising domains. Our computational experiments demonstrate that heuristic approaches, on average, yield suboptimal solutions with at least a 20% relative gap with those obtained by the MILP formulation.<\/jats:p>","DOI":"10.1007\/s11590-024-02130-z","type":"journal-article","created":{"date-parts":[[2024,6,24]],"date-time":"2024-06-24T19:00:39Z","timestamp":1719255639000},"page":"1771-1789","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strategy investments in zero-sum games"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1559-6612","authenticated-orcid":false,"given":"Raul","family":"Garcia","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7016-5925","authenticated-orcid":false,"given":"Seyedmohammadhossein","family":"Hosseinian","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9989-6676","authenticated-orcid":false,"given":"Mallesh","family":"Pai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0379-741X","authenticated-orcid":false,"given":"Andrew J.","family":"Schaefer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,24]]},"reference":[{"key":"2130_CR1","volume-title":"Linear Programming","author":"V Chv\u00e1tal","year":"1983","unstructured":"Chv\u00e1tal, V.: Linear Programming. W.H. Freeman and Company, New York (1983)"},{"issue":"1","key":"2130_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/BF01448847","volume":"100","author":"J Neumann","year":"1928","unstructured":"Neumann, J.: Zur theorie der gesellschaftsspiele. Mathematische annalen 100(1), 295\u2013320 (1928)","journal-title":"Mathematische annalen"},{"key":"2130_CR3","volume-title":"Game Theory","author":"AR Karlin","year":"2017","unstructured":"Karlin, A.R., Peres, Y.: Game Theory. Alive. American Mathematical Society, Providence (2017)"},{"key":"2130_CR4","unstructured":"Pita, J., Jain, M., Marecki, J., Ord\u00f3\u00f1ez, F., Portway, C., Tambe, M., Western, C., Paruchuri, P., Kraus, S.: Deployed armor protection: The application of a game theoretic model for security at the los angeles international airport. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems: Industrial Track, pp. 125\u2013132 (2008)"},{"key":"2130_CR5","unstructured":"Shieh, E., Bo\u00a0An, R.Y., Milind\u00a0Tambe, C.B., DiRenzo, J., Maule, B., Meyer, G.: Protect: A deployed game theoretic system to protect the ports of the united states. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, pp. 13\u201320 (2012)"},{"key":"2130_CR6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511973031","volume-title":"Security and Game Theory: Algorithms, Deployed Systems","author":"M Tambe","year":"2011","unstructured":"Tambe, M.: Security and Game Theory: Algorithms, Deployed Systems. Lessons Learned. Cambridge University Press, New York (2011)"},{"key":"2130_CR7","doi-asserted-by":"crossref","unstructured":"Yin, Z., Jiang, A., Johnson, M., Tambe, M., Kiekintveld, C., Leyton-Brown, K., Sandholm, T., Sullivan, J.: TRUSTS: Scheduling randomized patrols for fare inspection in transit systems. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 26, pp. 2348\u20132355 (2012)","DOI":"10.1609\/aaai.v26i2.18975"},{"key":"2130_CR8","unstructured":"Tsai, J., Rathi, S., Kiekintveld, C., Ordonez, F., Tambe, M.: IRIS - A Tool for Strategic Security Allocation in Transportation Networks. In: International Conference on Autonomous Agents and Multiagent Systems\u2014Industry Track, pp. 37\u201344 (2009)"},{"key":"2130_CR9","unstructured":"Yang, R., Ford, B.J., Tambe, M., Lemieux, A.: Adaptive resource allocation for wildlife protection against illegal poachers. In: Aamas, pp. 453\u2013460 (2014)"},{"key":"2130_CR10","unstructured":"Gerace, D.: A look at how airport security has evolved post, pp. 9\u201311. https:\/\/www.phl.org\/newsroom\/911-security-impact (2021)"},{"key":"2130_CR11","unstructured":"Transportation Security Administration: Security Screening. https:\/\/www.tsa.gov\/travel\/security-screening (2023)"},{"key":"2130_CR12","doi-asserted-by":"crossref","unstructured":"Jones, K., Shao, B., Blass, D.: Case study: Implications of installing vehicle security barriers in elevated structural slabs. In: Structures Congress 2020, pp. 11\u201323. American Society of Civil Engineers Reston, VA (2020)","DOI":"10.1061\/9780784482896.002"},{"issue":"1","key":"2130_CR13","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/130915303","volume":"57","author":"JP Vielma","year":"2015","unstructured":"Vielma, J.P.: Mixed integer linear programming formulation techniques. SIAM Rev. 57(1), 3\u201375 (2015)","journal-title":"SIAM Rev."},{"key":"2130_CR14","unstructured":"Wolsey, L.A., Nemhauser, G.L.: Integer and Combinatorial Optimization, vol. 55. John Wiley & Sons, New York (1999)"},{"key":"2130_CR15","doi-asserted-by":"crossref","unstructured":"Conitzer, V., Sandholm, T.: Computing the optimal strategy to commit to. In:Proceedings of the 7th ACM Conference on Electronic Commerce, pp. 82\u201390 (2006)","DOI":"10.1145\/1134707.1134717"},{"key":"2130_CR16","unstructured":"Gurobi Optimization, LLC: Gurobi Optimizer Reference Manual. https:\/\/www.gurobi.com (2023)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-024-02130-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-024-02130-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-024-02130-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,5]],"date-time":"2024-10-05T09:13:26Z","timestamp":1728119606000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-024-02130-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,24]]},"references-count":16,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["2130"],"URL":"https:\/\/doi.org\/10.1007\/s11590-024-02130-z","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"type":"print","value":"1862-4472"},{"type":"electronic","value":"1862-4480"}],"subject":[],"published":{"date-parts":[[2024,6,24]]},"assertion":[{"value":"30 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}