# American Institute of Mathematical Sciences

January  2022, 9(1): 33-74. doi: 10.3934/jdg.2021024

## Explaining the definition of wholesale access prices in the Portuguese telecommunications industry

 1 Economics Department, Faculty of Economics, University of Porto, Porto, Portugal 2 Rua Dr. Roberto Frias, N/A, 4200-464 Porto, Portugal 3 Electrical and Computer Engineering Department, Faculty of Engineering, University of Porto

* Corresponding author: Vitor Miguel Ribeiro

Received  February 2021 Revised  August 2021 Published  January 2022 Early access  October 2021

Fund Project: Authors were supported by the following projects and grants: DigEcoBus - NORTE-01-0145-FEDER-028540, STRIDE - NORTE-01-0145-FEDER-000033, Emprego altamente qualificado nas empresas ou em COLABS e/ou Contratação de Recursos Humanos Altamente Qualificados - NORTE-06-3559-FSE-0000164, and 2020 AI for COVID-19 Data Science and Artificial Intelligence - DSAIPA-CS-0086-2020. This research has also been financed by Portuguese public funds through FCT - Fundação para a Ciência e a Tecnologia, I.P., in the framework of R & D Units SYSTEC - reference POCI-01-0145-FEDER-006933 and Cef.UP - reference UIDB/04105/2020

The 2016–2018 triennium was a period marked by a fierce dispute between the European Commission and Autoridade Nacional de Comunicações, Portugal, on the need to regulate wholesale access prices. While the European Commission defended the imposition of Fiber-To-The-x regulation in non-competitive areas, the Portuguese sectoral regulator argued in favor of the persistence of Fiber-To-The-x deregulation. Following a Game Theory approach, the present study demonstrates that the transition from Fiber-To-The-x deregulation to Fiber-To-The-x regulation should only occur when a given territorial unit becomes a competitive area since the subgame perfect Nash equilibrium captures a regulatory framework optimally characterized by the imposition of active access price deregulation (regulation) in non-competitive (competitive) areas, that is, local administrative units characterized by a weak (strong) degree of vertical spillover, respectively. Meanwhile, ducts access regulation must be permanently imposed throughout the national territory, despite it can be relaxed in competitive areas if the regulator imposes intra-flexibility to establish a monopolistic bottleneck to ensure social welfare maximization. Previous conclusions require to introduce both facility-based and service-based competition at the entry stage as well as active and passive obligations at the regulation stage in a multi-stage game with complete information. The present analysis legitimizes the emergence of a new optimization theory in the telecommunications literature, whose modus operandi is contrary to (coincident with) the ladder of investment theory in non-competitive (competitive) areas, respectively. Differently from the view sustained by the ladder of investment theory, which defends that a short-term regulatory touch combined with long-term market deregulation is a socially optimal strategy, the new theory confirms that a regulatory intervention is socially desirable only in the long run. The conceptual refinement is meticulously explained and labeled as the theory of creative creation because, differently from the Schumpeterian gale of creative destruction, whose processes of industrial mutation are permanently market-driven by assumption, a period of regulatory holidays followed by successive regulatory interventions dependent on the degree of vertical spillover observed in the telecommunications industry can effectively promote investment realization that continuously revolutionizes the market structure from within, incessantly destroying the old technology. The theory of creative creation reflects the regulatory framework currently in force in the Portuguese Telecommunications Industry.

Citation: Vitor Miguel Ribeiro, Fernando Lobo Pereira, Rui Gonçalves. Explaining the definition of wholesale access prices in the Portuguese telecommunications industry. Journal of Dynamics and Games, 2022, 9 (1) : 33-74. doi: 10.3934/jdg.2021024
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Equilibrium number of facility-based competitors. Red line represents the number of facility-based firms in NC areas. Gray line represents the number of facility-based firms that would be sustained in case of FTTx regulation in the subdomain $0\leq\beta<0.4476.$ Black (Blue) line represents the number of facility-based firms in C areas when the duopolistic bottleneck with asymmetric downstream access (monopolistic bottleneck) is sustained in equilibrium, respectively
Equilibrium wholesale access prices. Red (Blue) [Black] lines represent the parameter space where the triopoly (monopolistic bottleneck) [duopolistic bottleneck with asymmetric downstream access] is sustained in equilibrium, respectively. Continuous (Dashed) lines represent the regulated active access price (ducts access fee), respectively. The plot assumes $a = 1$
Equilibrium investment level of the facility-based operators. Red (Blue) [Black] lines represent the parameter space where the triopoly (monopolistic bottleneck) [duopolistic bottleneck with asymmetric downstream access] is sustained in equilibrium, respectively. Continuous (Dashed) [Dotted] lines represent investment level of the incumbent (first alternative facility-based) [second alternative facility-based] operator, respectively. The right middle panel compares the profit level of the facility-based competitors I and N. Gray lines represent the investment level that would be achieved if FTTx regulation were adopted in the subdomain $0\leq\beta<0.4476$. The last subplot captures the total amount of investment in the telecommunications industry. The plot assumes $a = 1$
Equilibrium prices and quantities in the retail market. Red (Blue) [Black] lines represent the parameter space where the triopoly (monopolistic bottleneck) [duopolistic bottleneck with asymmetric downstream access] holds in equilibrium, respectively. Continuous (Dashed) [Dotted] lines represent retail prices and market share of the incumbent (alternative facility-based) [alternative service-based] operator, respectively. The plot assumes $a = 1$
Equilibrium profits. Red (Blue) [Black] lines represent the parameter space where the triopoly (monopolistic bottleneck) [duopolistic bottleneck with asymmetric downstream access] is sustained in equilibrium, respectively. Continuous (Dashed) [Dotted] lines represent profit of the incumbent (alternative facility-based) [alternative service-based] operator, respectively. The left bottom panel compares the profit level of the facility-based competitors I and N. Gray lines represent the profit level that would be obtained if FTTx regulation were adopted in the subdomain $0\leq\beta<0.4476$. The plot assumes $a = 1$
Equilibrium consumer surplus, producer surplus and social welfare. Gray lines represent the level of social welfare that would be achieved if FTTx regulation were adopted in the subdomain $0\leq\beta<0.4476$. The deadweight loss in NC areas corresponds to the space between the red and gray line in the subdomain $0\leq\beta<0.4476$ that can be observed in the right bottom panel. The plot assumes $a = 1$
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