# The Interplay of Competition and Cooperation Among Service Providers (Part I)

## TL;DR

This paper models the strategic interactions among mobile network operators and virtual operators, analyzing how spectrum acquisition influences competition and cooperation, with implications for provider payoffs and consumer benefits.

## Contribution

It provides a comprehensive game-theoretic analysis of spectrum sharing scenarios among MNOs and MVNOs, deriving explicit equilibrium characterizations and metrics for cooperation and competition.

## Key findings

- Cooperation between MNO and MVNO can increase both parties' payoffs.
- Additional MNOs enhance consumer benefits but reduce provider payoffs.
- Equilibrium strategies are easy to compute and characterized in closed form.

## Abstract

This paper investigates the incentives of mobile network operators (MNOs) for acquiring additional spectrum to offer mobile virtual network operators (MVNOs) and thereby inviting competition for a common pool of end users (EUs). We consider a base case and two generalizations: (i) one MNO and one MVNO, (ii) one MNO, one MVNO and an outside option, and (iii) two MNOs and one MVNO. In each of these cases, we model the interactions of the service providers (SPs) using a sequential game, identify when the Subgame Perfect Nash Equilibrium (SPNE) exists, when it is unique and characterize the SPNE when it exists. The characterizations are easy to compute, and are in closed form or involve optimizations in only one decision variable. We identify metrics to quantify the interplay between cooperation and competition, and evaluate those as also the SPNEs to show that cooperation between MNO and MVNO can enhance the payoffs of both, while increased competition due to the presence of additional MNOs is beneficial to EUs but reduces the payoffs of the SPs.