Nash's bargaining problem and the scale-invariant Hirsch citation index

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dc.authorid0000-0002-8213-3987
dc.contributor.authorFreixas, Josep
dc.contributor.authorHoerl, Roger
dc.contributor.authorZwicker, William S.
dc.date.accessioned2026-04-04T18:55:23Z
dc.date.available2026-04-04T18:55:23Z
dc.date.issued2025
dc.departmentİstanbul Bilgi Üniversitesi
dc.description.abstractA number of citation indices have been proposed for measuring and ranking the research publication records of scholars. Some of the best known indices, such as those proposed by Hirsch and Woeginger, are designed to reward most highly those records that strike some balance between productivity (number of papers published) and impact (frequency with which those papers are cited). A large number of rarely cited publications will not score well, nor will a very small number of heavily cited papers. We discuss three new citation indices, one of which was independently proposed in Fenner et al. (PLOS ONE 13(7): e0200098, 2018). Each rests on the notion of scale invariance, fundamental to John Nash's solution of the two-person bargaining problem. Our main focus is on one of these-a scale-invariant version of the Hirsch index. We argue that it has advantages over the original; it produces fairer rankings within subdisciplines, is more decisive (discriminates more finely, yielding fewer ties) and more dynamic (growing over time via more frequent, smaller increments), and exhibits enhanced centrality and tail balancedness. Simulations suggest that scale invariance improves robustness under Poisson noise, with increased decisiveness having no cost in terms of the number of accidental reversals, wherein random irregularities cause researcher A to receive a lower index value than B, although A's productivity and impact are both slightly higher than B's. Moreover, we provide an axiomatic characterization of the scale-invariant Hirsch index, via axioms that bear a close relationship, in discrete analogue, to those used by Nash (Econometrica 18(2):155-162, 1950). This argues for the mathematical naturality of the new index.
dc.description.sponsorshipMinisterio de Ciencia, Innovacin y Universidades [MCIN/AEI/10.13039/501100011033, PID2020-112581GB-C21]; CY Initiative of Excellence [ANR-16-IDEX-0008]
dc.description.sponsorshipThe first author's research was partially supported by MCIN/AEI/10.13039/501100011033 under grant PID2020-112581GB-C21 (MOTION). The third author's work was partially supported by the CY Initiative of Excellence (grant Investissements d'Avenir ANR-16-IDEX-0008) and was developed partly during the author's stay at CY Advanced Studies. We thank Denis Bouyssou for his informative comments, and the two referees for many helpful suggestions, all of which improved the manuscript.
dc.identifier.doi10.1007/s11238-025-10028-0
dc.identifier.doi10.1007/s11238-025-10028-0
dc.identifier.issn0040-5833
dc.identifier.issn1573-7187
dc.identifier.scopus2-s2.0-105000747041
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s11238-025-10028-0
dc.identifier.urihttps://hdl.handle.net/11411/10400
dc.identifier.wosWOS:001468399000001
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofTheory and Decision
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260402
dc.snmzKA_Scopus_20260402
dc.subjectScientific Citation Index
dc.subjectNash Bargaining Problem
dc.subjectHirsch Index
dc.subjectWoeginger Index
dc.subjectScale-Invariant Indices
dc.subjectChi-Index
dc.titleNash's bargaining problem and the scale-invariant Hirsch citation index
dc.typeArticle

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