Prague Economic Papers 2026, 35(1):97-120 | DOI: 10.18267/j.pep.905
The Reverse Banzhaf and Shapley - Shubik Index for SMEs in Slovak Medical Labs
- Zuzana Čičková (Corresponding author), Bratislava University of Economics and Business, Dolnozemská 1/b, 852 35 Bratislava, Slovakia
- Monika Ferenčáková, Bratislava University of Economics and Business, Dolnozemská 1/b, 852 35 Bratislava, Slovakia
- Peter Pe»ko, Bratislava University of Economics and Business, Dolnozemská 1/b, 852 35 Bratislava, Slovakia
This study examines the potential for cooperation between traditionally competitive small and medium-sized enterprises (SMEs) in the sector 86901 - Medical laboratory services in Slovakia as a strategy to enhance competitiveness in the face of large market players. By building coalitions, SMEs can overcome natural disadvantages, such as limited economies of scale, a lack of capital, or limited access to innovation. In this article, we will focus on the possibilities of applying the Banzhaf and Shapley - Shubik indices, as well as their reverse interpretation, to quantify the individual strength of a player within potential coalition groupings, with an emphasis on Slovak SMEs. The quantification of the indices considers key regulatory elements, including compliance with antitrust laws, and these legal frameworks are crucial for promoting fair competition while enabling SMEs to reap the benefits of cooperation.
Klíčová slova: cooperation, market share, strength indicators, game theory, Banzhaf index, Shapley - Shubik index
JEL classification: C71, K21, L13, L26
Vloľeno: 26. září 2025; Revidováno: 12. leden 2026; Přijato: 19. leden 2026; Zveřejněno: 1. duben 2026 Zobrazit citaci
Reference
- Act No. 187/2021 Coll. on the Protection of Economic Competition and on Amendments and Supplements to Certain Acts of the National Council of the Slovak Republic (s.f.).
- Álvarez-Mozos, M. and Tejada, O., 2011. Parallel characterizations of a generalized Shapley value and a generalized Banzhaf. Decision Support Systems, 52(1), pp. 21-27. https://doi.org/10.1016/j.dss.2011.04.005
Přejít k původnímu zdroji... - Auditors, E. C. o., 2020. The Commission's control procedures, Luxembourg: EU Publications Office. https://op.europa.eu/webpub/eca/annual-activity-report-2020/en/
- Banzhaf, J. F., 1965. Weighted Voting Doesn't Work: A Mathematical Analysis. Rutgers Law Review, Volumen 19, pp. 317-343. http://dx.doi.org/10.4236/sm.2013.32022
Přejít k původnímu zdroji... - Beck, T., Demirguc-Kunt, A. and Maksimovic, V., 2005. Financial and legal constraints to firm growth - Does size matter?. Journal of Finance, 60(1), pp. 137-177. https://doi.org/10.1111/j.1540-6261.2005.00727.x
Přejít k původnímu zdroji... - Bedi, S. and Vij, S., 2019. Post-Merger Integration Challenges in Lafarge-Holcim Merger. Pacific Business Review International, 11(9), pp. 62-76. https://www.pbr.co.in/2019/2019_month/march/6.pdf
- Brandenburger, A. M. and Nalebuff, B. J., 1996. Co-Opetition. s.l.:Harvard Business School Press. https://doi.org/10.4236/ojbm.2024.122071
Přejít k původnímu zdroji... - Commision, E., 2024. Annual Report on European SMEs 2023/2024, Luxembourg: Publications Office of the European Union. https://dx.doi.org/10.2826/355464
Přejít k původnímu zdroji... - Commission, E., 2024. The Draghi report on EU competitiveness, Brussel: European Commission. https://doi.org/10.2872/9356120
Přejít k původnímu zdroji... - Dlouhý, M. and Fiala, P., 2015. Teorie ekonomických a politických her. Praha: Vysoká ąkola ekonomická v Praze. https://doi.org/10.18267/pu.2015.dlo.2124.4
Přejít k původnímu zdroji... - Edwards, J. S. and Weichenrieder, A. J., 2009. Control rights, pyramids, and the measurement of ownership concentration. Journal of Economic Behavior & Organization, 72(1), pp. 489-508. https://doi.org/10.1016/j.jebo.2009.05.016
Přejít k původnímu zdroji... - European Union, 2016. Treaty on the Functioning of the European Union, s.l.: Official Journal of the European Union. https://eur-lex.europa.eu/eli/treaty/tfeu_2016/oj/eng
- European_Commision, 2025. Commission work programme 2025, Strasbourg: s.n.
- Feltkamp, V., 1995. Alternative axiomatic characterizations of the Shapley and Banzhaf values. International Journal of Game Theory, 24(2), pp. 179-186. https://doi.org/10.1007/BF01240041
Přejít k původnímu zdroji... - Haake, C.-J. and Schneider, M. R., 2024. Playing games with QCA: The Banzhaf index as a context-sensitive measure of explanatory power in international management. Journal of International Management, 30(2). https://doi.org/10.1016/j.intman.2023.101065
Přejít k původnímu zdroji... - Holubčík, M. and Soviar, J., 2021. Main Problems of Cooperation Management: Insights from Slovak Companies. Sustainability, 13(12), pp. 1-19. https://doi.org/10.3390/su13126736
Přejít k původnímu zdroji... - Keijzer, B. d., Klos, T. and Zhang, Y., 2010. Enumeration and exact design of weighted voting games. ACM Transactions on Intelligent Systems and Technology, 3(4), pp. 1-26. https://doi.org/10.1145/1838206.1838261
Přejít k původnímu zdroji... - Kovacic, W. E. and Shapiro, C., 2000. Antitrust Policy: A Century of Economic and Legal Thinking. Journal of Economic Perspectives, 14(1), p. 43-60. https://doi.org/10.1257/jep.14.1.43
Přejít k původnímu zdroji... - Letta, E., 2024. MUCH MORE THAN A MARKET, s.l.: s.n.
- Nagarajan, M. and Soąić, G., 2007. Stable Farsighted Coalitions in Competitive Markets. Management Science, 53(1), pp. 29-45. https://doi.org/10.1287/mnsc.1060.0605
Přejít k původnímu zdroji... - SARIO, 2024. Pharmaceutical & Life Sciences Sector in SLOVAKIA, Bratislava: SLOVAK INVESTMENT AND TRADE DEVELOPMENT AGENCY. https://www.sario.sk/en/invest-slovakia/industries-regions-overviews/pharmaceutical-life-sciences-industry
- Shapley, L. S. and Shubik, M., 1954. A Method for Evaluating the Distribution of Power in a Committee System. American Political Science Review, 48(3), p. 787-792. https://doi.org/10.2307/1951053
Přejít k původnímu zdroji...
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