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 ORCID..., Monika Ferenčáková, Peter Pe»ko
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.

Keywords: cooperation, market share, strength indicators, game theory, Banzhaf index, Shapley - Shubik index
JEL classification: C71, K21, L13, L26

Received: September 26, 2025; Revised: January 12, 2026; Accepted: January 19, 2026; Published: April 1, 2026  Show citation

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Čičková, Z., Ferenčáková, M., & Pe»ko, P. (2026). The Reverse Banzhaf and Shapley - Shubik Index for SMEs in Slovak Medical Labs. Prague Economic Papers, 35(1), 97-120. doi: 10.18267/j.pep.905
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    References

    1. 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.).
    2. 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 Go to original source...
    3. 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/
    4. 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 Go to original source...
    5. 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 Go to original source...
    6. 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
    7. Brandenburger, A. M. and Nalebuff, B. J., 1996. Co-Opetition. s.l.:Harvard Business School Press. https://doi.org/10.4236/ojbm.2024.122071 Go to original source...
    8. Commision, E., 2024. Annual Report on European SMEs 2023/2024, Luxembourg: Publications Office of the European Union. https://dx.doi.org/10.2826/355464 Go to original source...
    9. Commission, E., 2024. The Draghi report on EU competitiveness, Brussel: European Commission. https://doi.org/10.2872/9356120 Go to original source...
    10. 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 Go to original source...
    11. 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 Go to original source...
    12. 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
    13. European_Commision, 2025. Commission work programme 2025, Strasbourg: s.n.
    14. 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 Go to original source...
    15. 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 Go to original source...
    16. 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 Go to original source...
    17. 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 Go to original source...
    18. 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 Go to original source...
    19. Letta, E., 2024. MUCH MORE THAN A MARKET, s.l.: s.n.
    20. 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 Go to original source...
    21. 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
    22. 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 Go to original source...

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