Co-Investment under Revenue Uncertainty Based on Stochastic Coalitional Game Theory

Jul 16, 2026

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The deployment of new services such as Mobile Edge Computing (MEC) requires large upfront investment that rarely fits a single party’s budget. A co-investment mechanism is proposed in which the Infrastructure Provider (InP) and multiple Service Providers (SPs) form the grand coalition to share costs and revenues while maximizing their payoffs. Stochastic coalitional game theory is used to obtain probability lower bounds for grand-coalition stability, and profitability-based conditions prevent overly conservative outcomes under dependent revenue fluctuations. Results for MEC show strong stability lower bounds when SP revenues are comparable, while profit remains feasible even when revenues are highly variable.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages62

Reading Time2 h 36 min

Abstract

Keywords

Introduction

Economic barrier and stakeholder roles

MEC deployment setting and challenges

arXiv :2510 . 14555v2 [ cs .GT] 10 Jul 2026 Co-Investment under Revenue Uncertainty Based on Stochastic Coalitional Game Theory Amal Sakr 1*, Andrea Araldo 1 , Tijani Chahed 1 , Daniel Kofman2 1* SAMOVAR, T´el´ecom SudParis, Institut Polytechnique de Paris, 91120 Palaiseau, France. 2 T´el´ecom Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France. *Corresponding author(s). E-mail(s): [amal.sakr@telecom-sudparis.eu](amal.sakr@telecom-sudparis.eu) ; Contributing authors: [andrea.araldo@telecom-sudparis.eu](andrea.araldo@telecom-sudparis.eu) ; [tijani.chahed@telecom-sudparis.eu](tijani.chahed@telecom-sudparis.eu) ; [daniel.kofman@telecom-paristech.fr](daniel.kofman@telecom-paristech.fr) ; Abstract 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 coinvestment 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 highly dependent 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, and we derive a lower bound on the probability that co-investment is proﬁtable. 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, 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. 1 Keywords: Co-investment, Uncertainty, Coalitional game, Stability, Proﬁtability, Mobile Edge Computing 1 Introduction Several examples exist of technologies that, from a purely technical point of view, would be ready to emerge or scale up, but whose development is hindered by a big economic barrier. This is the case of technologies requiring the deployment of a massive infrastructure, for which massive investments need to be engaged upfront, and whose precise future proﬁts remain uncertain. We call Infrastructure Provider (InP) the actor responsible for deploying, maintaining and operating the physical infrastructure. We consider that, on top of such an infrastructure, third-party Service Providers (SPs) run their applications and collect revenues from end users. An example of this setting is the electric vehicle charging infrastructure (Badia et al. 2019), where the electric grid operator, acting as the InP, is tasked with deploying the grid infrastructure, e.g., bringing high-capacity electricity lines to road networks. On top of such grid infrastructure, electric vehicle charging station providers, which take the role of SPs, can operate their business and get revenues from end-users (drivers) (Fredriksson et al. 2019) . Another example, which is also the one we consider in the numerical results, involves the deployment and operation of Mobile Edge Computing (MEC) (Satyanarayanan 2017) . MEC is a computing architecture that decentralizes data processing by bringing it to the edge of the network, e.g., base stations (Shi et al. 2016) . This proximity to end-users reduces latency, improves bandwidth eﬃcie

FAQs

What is the main challenge addressed by the co-investment scheme?

Future revenues from edge services are uncertain, which makes it difficult for a single stakeholder to justify the large upfront investment required for deployment.

Who are the players in the proposed grand coalition?

The grand coalition consists of the Infrastructure Provider (InP) and multiple Service Providers (SPs), jointly sharing costs and revenues.

How does the framework handle highly dependent fluctuations of revenues?

When dependencies make stability too conservative, the framework adds profitabilty as a necessary condition and derives a probability lower bound for co-investment to be profitable.

Jul 16, 2026

Upload by Patrick