The introduction of new services, such as Mobile Edge Computing (MEC), requires a massive investment that cannot be assumed by a single stakeholder, for instance the Infrastructure Provider (InP). Service Providers (SPs) however also have an interest in the deployment of such services. We hence propose a co-investment scheme in which all stakeholders, i.e., the InP and the SPs, form the so-called grand coalition composed of all the stakeholders with the aim of sharing costs and revenues and maximizing their payoffs. The challenge comes from the fact that future revenues are uncertain. We devise in this case a novel stochastic coalitional game formulation which builds upon robust game theory and derive a lower bound on the probability of the stability of the grand coalition, wherein no player can be better off outside of it. In the presence of some correlated fluctuations of revenues however, stability can be too conservative. In this case, we make use also of profitability, in which payoffs of players are non-negative, as a necessary condition for co-investment. The proposed framework is showcased for MEC deployment, where computational resources need to be deployed in nodes at the edge of a telecommunication network. Numerical results show high lower bound on the probability of stability when the SPs' revenues are of similar magnitude and the investment period is sufficiently long, even with high levels of uncertainty. In the case where revenues are highly variable however, the lower bound on stability can be trivially low whereas co-investment is still profitable.

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