{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:31:08Z","timestamp":1787322668706,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We consider a caching game in which a unit amount of infinitely divisible material is distributed among $n\\geq 2$ locations. A Searcher chooses how to distribute his search effort $r$ about the locations so as to maximize the probability she will find a given minimum amount $\\bar{m} =1-m\\leq r$ of the material. If the search effort $y_{i}$ invested by the Searcher in a given location $i$ is at least as great as the amount of material $x_{i}$ located there she finds all of it, otherwise the amount she finds is only $y_{i}$. In other words she finds $\\min \\left\\{ x_{i},y_{i}\\right\\} $ in location $i$. We seek the randomized distribution of search effort that maximizes the probability of success for the Searcher in the worst case, hence we model the problem as a zero-sum win-lose game between the Searcher and a malevolent Hider who wishes to keep more than $m$ of the material. We show that in the case $r=\\bar{m}$ the game has a geometric interpretation that for $n=2$ corresponds to a problem posed by W. H. Ruckle in his monograph [Geometric Games and Their Applications, Pitman, Boston, 1983]. We give solutions for the geometric game when $n=3$ for certain values of $m$, and bounds on the value for other values of $m$. In the more general case $r\\geq \\bar{m}$ we show that for $n=2$ the game reduces to Ruckle's game.<\/jats:p>","DOI":"10.1137\/140997075","type":"journal-article","created":{"date-parts":[[2015,9,15]],"date-time":"2015-09-15T13:46:10Z","timestamp":1442324770000},"page":"3040-3056","source":"Crossref","is-referenced-by-count":0,"title":["A Caching Game with Infinitely Divisible Hidden Material"],"prefix":"10.1137","volume":"53","author":[{"given":"Thomas","family":"Lidbetter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,9,15]]},"reference":[{"key":"atypb1","first-page":"10","volume":"59","author":"Alon N.","year":"2009","journal-title":"IEEE Inform. Theory Soc. Newsletter"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/net.21555"},{"key":"atypb3","first-page":"220","author":"Alpern S.","year":"2010","journal-title":"New York"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/080741926"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2011.0581"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/0326077"},{"key":"atypb7","unstructured":"S. Alpern and S. Gal,\n                      The Theory of Search Games and Rendezvous,\n                      Internat. Ser. Oper. Res. Management Sci. 319, Kluwer Academic, Boston, 2003."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.2307\/1906813"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2011.02.009"},{"key":"atypb10","unstructured":"S. Artstein-Avidan and B. A. Slomka,\n                      On weighted covering numbers and the Levi-Hadwiger conjecture\n                      , preprint, arXiv:1310.7892, 2013."},{"key":"atypb11","first-page":"85","author":"Baston V.","year":"2014","journal-title":"New York"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1080.0570"},{"key":"atypb13","doi-asserted-by":"crossref","first-page":"R37","DOI":"10.37236\/761","volume":"15","author":"Dumitrescu A.","year":"2008","journal-title":"Electron. J. Combin."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(75)90099-0"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"A. Garnaev,\n                      Search Games and Other Applications of Game Theory,\n                      Lecture Notes in Econom. and Math. Systems 485, Springer-Verlag, Berlin, 2000.","DOI":"10.1007\/978-3-642-57304-0"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-5915.1988.tb00275.x"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022639813629"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004609529766"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1002\/nav.1048"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.jors.2601077"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693169"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176342467"},{"key":"atypb23","unstructured":"W. Ruckle,\n                      Geometric Games and Their Applications,\n                      Pitman, Boston, 1983."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.08.005"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/140997075","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:24:12Z","timestamp":1787318652000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/140997075"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1137\/140997075"],"URL":"https:\/\/doi.org\/10.1137\/140997075","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}