{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:55:34Z","timestamp":1760147734086,"version":"build-2065373602"},"reference-count":78,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"WSB University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The purpose of this paper is to introduce new methods to measure the indirect control power of firms in complex corporate shareholding structures using the concept of power indices from cooperative game theory. The proposed measures vary in desirable properties satisfied, as well as in the bargaining models of power indices used to construct them. Hence, they can be used to produce different pictures of the coalitional strength of firms in control of other firms in mutual shareholding networks with the presence of cycles. Precisely, in the framework of Karos and Peters from 2015, ten power indices substitute the original Shapley and Shubik power index in a modular fashion. In this way, we obtain a set of new measures called aggregated indices. The float shareholders typically hold less than 5 percent of the outstanding shares, which is an uncertain element of indirect control in complex shareholding structures. The fuzzy number seems appropriate to model these shareholders\u2019 behavior. The novelty is that we model the behavior of float using Z-fuzzy numbers. The new methods are tested in an example.<\/jats:p>","DOI":"10.3390\/e25030429","type":"journal-article","created":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T02:28:09Z","timestamp":1677551289000},"page":"429","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Aggregated Power Indices for Measuring Indirect Control in Complex Corporate Networks with Float Shareholders"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9243-8653","authenticated-orcid":false,"given":"Izabella","family":"Stach","sequence":"first","affiliation":[{"name":"Faculty of Management, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7278-0155","authenticated-orcid":false,"given":"Jacek","family":"Mercik","sequence":"additional","affiliation":[{"name":"Faculty of Finance and Management, WSB University in Wroc\u0142aw, Fabryczna 29-31, 53-609 Wroc\u0142aw, Poland"}]},{"given":"Cesarino","family":"Bertini","sequence":"additional","affiliation":[{"name":"Department of Management, University of Bergamo, Via dei Caniana 2, 24127 Bergamo, Italy"}]},{"given":"Barbara","family":"G\u0142adysz","sequence":"additional","affiliation":[{"name":"Department of Operations Research and Business Intelligence, Faculty of Management, Wroc\u0142aw University of Science and Technology, Wybrze\u017ce Wyspia\u0144skiego 27, 50-370 Wroc\u0142aw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0619-4606","authenticated-orcid":false,"given":"Jochen","family":"Staudacher","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t Informatik, Kempten University, Bahnhofstr. 61, 87435 Kempten, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.geb.2015.06.003","article-title":"Indirect control and power in mutual control structures","volume":"92","author":"Karos","year":"2015","journal-title":"Games Econ. 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