{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T17:57:31Z","timestamp":1715709451322},"reference-count":37,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Operations Research"],"published-print":{"date-parts":[[2018,8]]},"abstract":" We consider a competitive facility location problem on a network where consumers located on vertices wish to connect to the nearest facility. Knowing this, each competitor locates a facility on a vertex, trying to maximize market share. We focus on the two-player case and study conditions that guarantee the existence of a pure-strategy Nash equilibrium for progressively more complicated classes of networks. For general graphs, we show that attention can be restricted to a subset of vertices referred to as the central block. By constructing trees of maximal bi-connected components, we obtain sufficient conditions for equilibrium existence. Moreover, when the central block is a vertex or a cycle (for example, in cactus graphs), this provides a complete and efficient characterization of equilibria. In that case, we show that both competitors locate their facilities in a solution to the 1-median problem, generalizing a well-known insight arising from Hotelling\u2019s model. We further show that an equilibrium must solve the 1-median problem in other classes of graphs, including grids, which essentially capture the topology of urban networks. In addition, when both players select a 1-median, the solution must be at equilibrium for strongly-chordal graphs, generalizing a previously known result for trees. <\/jats:p> The electronic companion is available at https:\/\/doi.org\/10.1287\/opre.2017.1694 . <\/jats:p>","DOI":"10.1287\/opre.2017.1694","type":"journal-article","created":{"date-parts":[[2018,7,23]],"date-time":"2018-07-23T13:57:45Z","timestamp":1532354265000},"page":"1058-1067","source":"Crossref","is-referenced-by-count":6,"title":["Technical Note\u2014The Competitive Facility Location Problem in a Duopoly: Advances Beyond Trees"],"prefix":"10.1287","volume":"66","author":[{"given":"Yonatan","family":"Gur","sequence":"first","affiliation":[{"name":"Stanford University, Stanford, California, 94305"}]},{"given":"Daniela","family":"Saban","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, California, 94305"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6380-1516","authenticated-orcid":false,"given":"Nicolas E.","family":"Stier-Moses","sequence":"additional","affiliation":[{"name":"Universidad Torcuato Di Tella, Buenos Aires (1428), Argentina"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2003.09.004"},{"key":"B2","volume-title":"The Design and Analysis of Computer Algorithms","author":"Aho AV","year":"1974"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1137\/S089548019936360X"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-77105-0_31"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.2307\/1912653"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5355-6_14"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5355-6"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9787.00094"},{"issue":"1","key":"B10","first-page":"7","volume":"42","author":"Eaton B","year":"1976","journal-title":"Rev. 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