{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:23:23Z","timestamp":1760235803624,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If, in a certain task group, a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.<\/jats:p>","DOI":"10.3390\/axioms10040247","type":"journal-article","created":{"date-parts":[[2021,10,1]],"date-time":"2021-10-01T10:55:40Z","timestamp":1633085740000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Axiomatic Characterizations of a Proportional Influence Measure for Sequential Projects with Imperfect Reliability"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2102-9323","authenticated-orcid":false,"given":"Andries","family":"van Beek","sequence":"first","affiliation":[{"name":"Department of Econometrics & Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Borm","sequence":"additional","affiliation":[{"name":"Department of Econometrics & Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marieke","family":"Quant","sequence":"additional","affiliation":[{"name":"Department of Econometrics & Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,30]]},"reference":[{"key":"ref_1","unstructured":"Lindelauf, R. (2011). Design and Analysis of Covert Networks, Affiliations and Projects. [Ph.D. Thesis, CentER, Tilburg School of Economics and Management, Tilburg University]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"866","DOI":"10.1287\/opre.1080.0643","article-title":"Interdicting a nuclear-weapons project","volume":"57","author":"Brown","year":"2009","journal-title":"Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s00182-006-0058-x","article-title":"Project games","volume":"36","author":"Borm","year":"2007","journal-title":"Int. J. Game Theory"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1016300218643","article-title":"How to distribute costs associated with a delayed project","volume":"109","year":"2002","journal-title":"Ann. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1023\/A:1016372707256","article-title":"Two approaches to the problem of sharing delay costs in joint projects","volume":"109","author":"Ferrari","year":"2002","journal-title":"Ann. Oper. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.socnet.2015.02.003","article-title":"Ranking terrorists in networks: A sensitivity analysis of Al Qaeda\u2019s 9\/11 attack","volume":"42","author":"Husslage","year":"2015","journal-title":"Soc. Netw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s40999-016-0011-8","article-title":"Quantitative risk allocation in construction projects using cooperative-bargaining game theory","volume":"14","author":"Nasirzadeh","year":"2016","journal-title":"Int. J. Civ. Eng."},{"key":"ref_8","first-page":"46","article-title":"Integrated project delivery an example of relational contracting","volume":"2","author":"Matthews","year":"2005","journal-title":"Lean Constr. J."},{"key":"ref_9","first-page":"32","article-title":"Using cooperative game theory to determine profit distribution in IPD projects","volume":"19","author":"Teng","year":"2019","journal-title":"Int. J. Constr. Manag."},{"key":"ref_10","first-page":"307","article-title":"A value for n-person games","volume":"2","author":"Shapley","year":"1953","journal-title":"Contrib. Theory Games"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/247\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:08:12Z","timestamp":1760166492000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/4\/247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,30]]},"references-count":10,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["axioms10040247"],"URL":"https:\/\/doi.org\/10.3390\/axioms10040247","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,9,30]]}}}