{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:08:05Z","timestamp":1760234885957,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["721846"],"award-info":[{"award-number":["721846"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002910","name":"F\u00e9d\u00e9ration Wallonie-Bruxelles","doi-asserted-by":"publisher","award":["15\/20-072"],"award-info":[{"award-number":["15\/20-072"]}],"id":[{"id":"10.13039\/501100002910","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002661","name":"Fonds De La Recherche Scientifique - FNRS","doi-asserted-by":"publisher","award":["T.0143.18"],"award-info":[{"award-number":["T.0143.18"]}],"id":[{"id":"10.13039\/501100002661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set to answer this question. We find that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsighted set whenever the degree of farsightedness of the criminals is larger than or equal to (n\u22121). Moreover, the complete network is the unique horizon-(n\u22121) farsighted set. Hence, the predictions obtained in case of completely farsighted criminals still hold when criminals are much less farsighted.<\/jats:p>","DOI":"10.3390\/g12030056","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T22:02:04Z","timestamp":1625522524000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Horizon-K Farsightedness in Criminal Networks"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1100-8601","authenticated-orcid":false,"given":"P. Jean-Jacques","family":"Herings","sequence":"first","affiliation":[{"name":"Department of Economics, Maastricht University, 6200 MD Maastricht, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4218-2127","authenticated-orcid":false,"given":"Ana","family":"Mauleon","sequence":"additional","affiliation":[{"name":"CEREC, UCLouvain Saint-Louis, 1000 Brussels, Belgium"},{"name":"CORE, UCLouvain, 1348 Louvain-la-Neuve, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Vannetelbosch","sequence":"additional","affiliation":[{"name":"CORE, UCLouvain, 1348 Louvain-la-Neuve, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.euroecorev.2007.09.002","article-title":"The strength of weak ties in crime","volume":"52","author":"Patacchini","year":"2008","journal-title":"Eur. 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PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0092276"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1111\/j.0020-6598.2004.00292.x","article-title":"Social networks and crime decisions: The role of social structure in facilitating delinquent behavior","volume":"45","author":"Zenou","year":"2004","journal-title":"Int. Econ. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1162\/jeea.2010.8.1.34","article-title":"Delinquent networks","volume":"8","author":"Ballester","year":"2010","journal-title":"J. Eur. Econ. Assoc."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Bezin, E., Verdier, T., and Zenou, Y. (2021). Crime, broken families and punishment. Am. Econ. J. Microecon., forthcoming.","DOI":"10.1257\/mic.20200379"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lee, L.-F., Liu, X., Patacchini, E., and Zenou, Y. (2021). Who is the key player? A network analysis of juvenile delinquency. J. Bus. Econ. Stat., forthcoming.","DOI":"10.1080\/07350015.2020.1737082"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.geb.2008.12.009","article-title":"Farsightedly stable networks","volume":"67","author":"Herings","year":"2009","journal-title":"Games Econ. Behav."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1006\/jeth.1994.1044","article-title":"Farsighted coalitional stability","volume":"63","author":"Chwe","year":"1994","journal-title":"J. Econ. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/s001990050204","article-title":"Coalitional stability under perfect foresight","volume":"11","author":"Xue","year":"1998","journal-title":"Econ. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.geb.2003.11.003","article-title":"Rationalizability for social environments","volume":"49","author":"Herings","year":"2004","journal-title":"Games Econ. Behav."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s11238-004-2646-1","article-title":"Farsightedness and cautiousness in coalition formation games with positive spillovers","volume":"56","author":"Mauleon","year":"2004","journal-title":"Theory Decis."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.jet.2004.05.001","article-title":"Farsighted network formation","volume":"122","author":"Dutta","year":"2005","journal-title":"J. Econ. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.jet.2004.02.007","article-title":"Networks and farsighted stability","volume":"120","author":"Page","year":"2005","journal-title":"J. Econ. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1016\/j.geb.2008.05.003","article-title":"Strategic basins of attraction, the path dominance core, and network formation games","volume":"66","author":"Page","year":"2009","journal-title":"Games Econ. Behav."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"499","DOI":"10.3982\/TE527","article-title":"von Neumann\u2013Morgernstern farsightedly stable sets in two-sided matching","volume":"6","author":"Mauleon","year":"2011","journal-title":"Theor. Econ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"977","DOI":"10.3982\/ECTA12022","article-title":"The farsighted stable set","volume":"83","author":"Ray","year":"2015","journal-title":"Econometrica"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s00199-018-1119-7","article-title":"Stability of networks under horizon-K farsightedness","volume":"68","author":"Herings","year":"2019","journal-title":"Econ. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"111","DOI":"10.3982\/ECTA14954","article-title":"The myopic stable set for social environments","volume":"87","author":"Demuynck","year":"2019","journal-title":"Econometrica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1006\/jeth.2001.2903","article-title":"The evolution of social and economic networks","volume":"106","author":"Jackson","year":"2002","journal-title":"J. Econ. 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