{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T14:27:02Z","timestamp":1773239222951,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,4,4]],"date-time":"2007-04-04T00:00:00Z","timestamp":1175644800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/2.0"},{"start":{"date-parts":[[2007,4,4]],"date-time":"2007-04-04T00:00:00Z","timestamp":1175644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc Choice Welfare"],"published-print":{"date-parts":[[2008,2]]},"DOI":"10.1007\/s00355-007-0230-7","type":"journal-article","created":{"date-parts":[[2007,4,3]],"date-time":"2007-04-03T10:27:15Z","timestamp":1175596035000},"page":"225-243","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Vertical wage differences in hierarchically structured firms"],"prefix":"10.1007","volume":"30","author":[{"given":"Ren\u00e9","family":"van den Brink","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,4,4]]},"reference":[{"key":"230_CR1","first-page":"777","volume":"62","author":"AA Alchian","year":"1972","unstructured":"Alchian AA, Demsetz H (1972) Production, information costs, and economic organization. Am Econ Rev 62:777\u2013795","journal-title":"Am Econ Rev"},{"key":"230_CR2","first-page":"317","volume":"19","author":"JF Banzhaf","year":"1965","unstructured":"Banzhaf JF (1965) Weighted voting doesn\u2019t work: a mathematical analysis. Rutgers Law Rev 19:317\u2013343","journal-title":"Rutgers Law Rev"},{"key":"230_CR3","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s003550000065","volume":"18","author":"R Ben-Yashar","year":"2001","unstructured":"Ben-Yashar R, Nitzan S (2001) The robustness of optimal organizational architectures: a Note on hierarchies and polyarchies. Soc Choice Welfare 18:155\u2013163","journal-title":"Soc Choice Welfare"},{"key":"230_CR4","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s001860200176","volume":"55","author":"R Br\u00e2nzei","year":"2002","unstructured":"Br\u00e2nzei R, Fragnelli V, Tijs S (2002) Tree connected peer group situations and peer group games. Math Methods Oper Res 55:93\u2013106","journal-title":"Math Methods Oper Res"},{"key":"230_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/BF01262510","volume":"26","author":"R van den Brink","year":"1997","unstructured":"van den Brink R (1997) An axiomatization of the disjunctive permission value for games with a permission structure. Int J Game Theory 26:27\u201343","journal-title":"Int J Game Theory"},{"key":"230_CR6","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1006\/game.1996.0008","volume":"12","author":"R van den Brink","year":"1996","unstructured":"van den Brink R, Gilles RP (1996) Axiomatizations of the conjunctive permission value for games with Permission Structures. Games Econ Behav 12:113\u2013126","journal-title":"Games Econ Behav"},{"key":"230_CR7","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s003550050125","volume":"15","author":"R van den Brink","year":"1998","unstructured":"van den Brink R, van der Laan G (1998) Axiomatizations of the normalized Banzhaf value and the Shapley value. Soc Choice Welfare 15:567-582","journal-title":"Soc Choice Welfare"},{"key":"230_CR8","doi-asserted-by":"crossref","unstructured":"van den Brink R, Ruys PHM (2005) Positional wages, market wages and firm size. Tinbergen Discussion Paper 05\/020-1, Tinbergen Institute and Free University, Amsterdam","DOI":"10.2139\/ssrn.678743"},{"key":"230_CR9","unstructured":"van den Brink R, Ruys PHM, Semenov R (2007) Governance of clubs and firms with cultural dimensions. Mimeo, Tinbergen Institute and Free University, Amsterdam"},{"key":"230_CR10","doi-asserted-by":"publisher","first-page":"943","DOI":"10.1086\/260719","volume":"86","author":"GA Calvo","year":"1978","unstructured":"Calvo GA, Wellisz S (1978) Supervision, loss of control, and the optimum size of the firm. J Pol Econ 86:943\u2013952","journal-title":"J Pol Econ"},{"key":"230_CR11","doi-asserted-by":"publisher","first-page":"991","DOI":"10.1086\/260809","volume":"87","author":"GA Calvo","year":"1979","unstructured":"Calvo GA, Wellisz S (1979) Hierarchy, ability and income distribution. J Pol Econ 87:991\u20131010","journal-title":"J Pol Econ"},{"key":"230_CR12","unstructured":"Carlson NW (1982) Time rates tighten their grip on manufacturing industries. Mon Labor Rev 15\u201322"},{"key":"230_CR13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1287\/moor.4.2.99","volume":"4","author":"P Dubey","year":"1979","unstructured":"Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4:99\u2013131","journal-title":"Math Oper Res"},{"key":"230_CR14","unstructured":"Gilles RP, Owen G (1994) Games with permission structures: The disjunctive approach. Mimeo, Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia"},{"key":"230_CR15","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/BF01253782","volume":"20","author":"RP Gilles","year":"1992","unstructured":"Gilles RP, Owen G, van den Brink R (1992) Games with permission structures: the conjunctive approach. Int J Game Theory 20:277\u2013293","journal-title":"Int J Game Theory"},{"key":"230_CR16","doi-asserted-by":"publisher","first-page":"7","DOI":"10.2307\/1912246","volume":"51","author":"SJ Grossman","year":"1983","unstructured":"Grossman SJ, Hart OD (1983) An analysis of the principal-agent problem. Econometrica 51:7\u201345","journal-title":"Econometrica"},{"key":"230_CR17","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1086\/261404","volume":"94","author":"SJ Grossman","year":"1986","unstructured":"Grossman SJ, Hart OD (1986) The costs and benefits of ownership: a theory of vertical and lateral integration. J Pol Econ 94:691\u2013719","journal-title":"J Pol Econ"},{"key":"230_CR18","doi-asserted-by":"publisher","first-page":"1119","DOI":"10.1086\/261729","volume":"98","author":"O Hart","year":"1990","unstructured":"Hart O, Moore J (1990) Property rights and the nature of the firm. J Polit Econ 98:1119\u20131158","journal-title":"J Polit Econ"},{"key":"230_CR19","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1111\/1467-937X.00080","volume":"66","author":"O Hart","year":"1999","unstructured":"Hart O, Moore J (1999) Foundations of incomplete contracts. Rev Econ Stud 66:115\u2013138","journal-title":"Rev Econ Stud"},{"key":"230_CR20","volume-title":"Culture\u2019s consequences. International differences in work-related values","author":"G Hofstede","year":"1980","unstructured":"Hofstede G (1980) Culture\u2019s consequences. International differences in work-related values. Sage Publications, Beverly Hills"},{"key":"230_CR21","doi-asserted-by":"publisher","first-page":"74","DOI":"10.2307\/3003320","volume":"10","author":"B Holmstr\u00f6m","year":"1979","unstructured":"Holmstr\u00f6m B (1979) Moral hazard and observability. Bell J Econ 10:74\u201391","journal-title":"Bell J Econ"},{"key":"230_CR22","volume-title":"The cooperative nature of the firm","author":"T Ichiishi","year":"1993","unstructured":"Ichiishi T (1993) The cooperative nature of the firm. Cambridge University Press, Cambridge"},{"key":"230_CR23","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/BF01756292","volume":"16","author":"E Kalai","year":"1987","unstructured":"Kalai E, Samet D (1987) On weighted Shapley values. Int J Game Theory 16:205\u2013222","journal-title":"Int J Game Theory"},{"key":"230_CR24","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1287\/mnsc.25.11.1162","volume":"25","author":"M Keren","year":"1979","unstructured":"Keren M, Levhari D (1979) The optimum span of control in a pure hierarchy. Manage Sci 25:1162\u20131172","journal-title":"Manage Sci"},{"key":"230_CR25","doi-asserted-by":"publisher","first-page":"474","DOI":"10.2307\/3003648","volume":"14","author":"M Keren","year":"1983","unstructured":"Keren M, Levhari D (1983) The internal organization of the firm and the shape of average costs. Bell J Econ 14:474\u2013486","journal-title":"Bell J Econ"},{"key":"230_CR26","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/s00355-003-0304-0","volume":"24","author":"WTH Koh","year":"2005","unstructured":"Koh WTH (2005) Optimal sequential decision architectures and the robustness of hierarchies and polyarchies. Soc Choice Welfare 24:397\u2013411","journal-title":"Soc Choice Welfare"},{"key":"230_CR27","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1023\/A:1004972127482","volume":"44","author":"G van der Laan","year":"1998","unstructured":"van der Laan G, van den Brink R (1998) An axiomated class of share functions for N-person games. Theory Decision 44:117\u2013148","journal-title":"Theory Decision"},{"key":"230_CR28","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1111\/1467-937X.00079","volume":"66","author":"E Maskin","year":"1999","unstructured":"Maskin E, Tirole J (1999) Unforeseen contingencies and incomplete contracts. Rev Econ Stud 66:83\u2013114","journal-title":"Rev Econ Stud"},{"key":"230_CR29","first-page":"511","volume":"80","author":"P Milgrom","year":"1994","unstructured":"Milgrom P, Roberts J (1994) The economics of modern manufacturing: technology, strategy and organization. Am Econ Rev 80:511\u2013528","journal-title":"Am Econ Rev"},{"key":"230_CR30","doi-asserted-by":"publisher","first-page":"741","DOI":"10.1002\/nav.3800220409","volume":"22","author":"G Owen","year":"1975","unstructured":"Owen G (1975) Multilinear extensions and the Banzhaf value. Nav Res Logis Q 22:741\u2013750","journal-title":"Nav Res Logis Q"},{"key":"230_CR31","first-page":"1382","volume":"30","author":"R Radner","year":"1992","unstructured":"Radner R (1992) Hierarchy: the economics of managing. J Econ Lit 30:1382\u20131415","journal-title":"J Econ Lit"},{"key":"230_CR32","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1162\/003355398555630","volume":"113","author":"RG Rajan","year":"1998","unstructured":"Rajan RG, Zingales L (1998) Power in a theory of the firm. Q J Econ 113:387\u2013432","journal-title":"Q J Econ"},{"key":"230_CR33","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1162\/00335530152466241","volume":"116","author":"RG Rajan","year":"2001","unstructured":"Rajan RG, Zingales L (2001) The firm as a dedicated hierarchy: a Theory of the origins and growth of firms. Q J Econ 116:805\u2013851","journal-title":"Q J Econ"},{"key":"230_CR34","first-page":"716","volume":"76","author":"RK Sah","year":"1986","unstructured":"Sah RK, Stiglitz JE (1986) The architecture of economic systems: hierarchies and polyarchies. Am Econ Rev 76:716\u2013727","journal-title":"Am Econ Rev"},{"key":"230_CR35","first-page":"307","volume-title":"Ann Math Stud 28 (Contributions to the theory of games Vol. 2)","author":"LS Shapley","year":"1953","unstructured":"Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Ann Math Stud 28 (Contributions to the theory of games Vol. 2). Princeton University Press, Princeton, pp 307\u2013317"},{"key":"230_CR36","doi-asserted-by":"publisher","first-page":"32","DOI":"10.2307\/2786111","volume":"20","author":"HA Simon","year":"1957","unstructured":"Simon HA (1957) The compensation of executives. Sociometry 20:32\u201335","journal-title":"Sociometry"},{"key":"230_CR37","volume-title":"The Shapley value: Essays in Honor of Lloyd S. Shapley","author":"RJ Weber","year":"1988","unstructured":"Weber RJ (1988) Probabilistic values for Games. In: Roth AE (ed) The Shapley value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press, Cambridge"},{"key":"230_CR38","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1086\/259258","volume":"75","author":"OE Williamson","year":"1967","unstructured":"Williamson OE (1967) Hierarchical control and optimum firm size. J Pol Econ 75:123\u2013138","journal-title":"J Pol Econ"}],"container-title":["Social Choice and Welfare"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-007-0230-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00355-007-0230-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-007-0230-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00355-007-0230-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T18:00:59Z","timestamp":1630432859000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00355-007-0230-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,4,4]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["230"],"URL":"https:\/\/doi.org\/10.1007\/s00355-007-0230-7","relation":{},"ISSN":["0176-1714","1432-217X"],"issn-type":[{"value":"0176-1714","type":"print"},{"value":"1432-217X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,4,4]]},"assertion":[{"value":"10 October 2005","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2007","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 April 2007","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}