arXiv subjects

Amal Sakr

Publications and source records attributed to Amal Sakr.

4 recordsLinked to original sources

arXiv2026

Shared Infrastructure Investment and Pricing: Stackelberg Equilibria in Risk-Aware Take-or-Pay Contracts

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms generating revenues through resource usage. We focus on a challenging setting where (i) infrastructure deployment requires substantial upfront investment, which the InP recovers via payments by firms that depend on their uncertain future revenues; (ii) firms' resource usage is jointly influenced by exogenous factors, infrastructure pricing, operational costs, and resource congestion; and (iii) firms exhibit heterogeneous risk aversion. These aspects are typical of emerging technologies, such as Mobile Edge Computing (MEC). Yet, their joint effect on the InP's capacity dimensioning and pricing decisions and the firms' usage commitments remains poorly understood. We establish conditions for the uniqueness of the equilibrium among the firms. We do so by introducing a Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader, while firms act as followers that share the infrastructure and commit upfront to future resource usage under uncertain revenues. Followers' heterogeneous risk aversion is modeled through Conditional Value-at-Risk (CVaR). We prove the existence of a Stackelberg equilibrium (SE), in which the followers' decisions constitute a generalized Nash equilibrium, and develop a polynomial-time algorithm that boundedly approximates the SE. We derive a lower bound on the followers' Probability of Profit (PoP). Simulations in a realistic MEC scenario show that higher followers' risk aversion reduces capacity, pricing, and leader profit, while increasing the lower bound on PoP.

cs.GT↗

arXiv2026

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

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 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.

cs.GT↗

arXiv2026

Continuity of VaR and Continuous Differentiability of CVaR under Decision-Dependent Losses

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are widely used in risk-aware optimization and equilibrium models. When the loss depends on a decision variable, the induced distribution, the VaR threshold, and the CVaR tail set all change with the decision. This makes the regularity of the VaR and CVaR maps nontrivial. We give simple sufficient conditions under which the VaR map is continuous and the corresponding CVaR map is continuously differentiable. The assumptions are local around the VaR level and rely on dominated pathwise differentiability of the scenario-wise loss. We also derive the CVaR gradient formula, thereby justifying first-order analysis for decision-dependent tail-risk models.

cs.GT↗

arXiv2026

Co-Investment in Mobile Edge Computing with Infrastructure Update and Dynamic Participation

Mobile Edge Computing (MEC) requires Network Operators (NOs) to undertake substantial infrastructure investments, while most revenues are captured by Service Providers (SPs) offering end-user applications. This cost-revenue imbalance discourages NOs from investing in MEC deployment, despite increasing demand for low-latency and bandwidth-intensive services. This paper proposes a co-investment scheme in which players, i.e., one NO and multiple SPs, jointly deploy, maintain, and share MEC infrastructure over multiple decision epochs. We devise a new coalitional game model that captures the planning of resources, their allocation among players, and cost and revenue sharing. To address fluctuating user demand and evolving participation incentives, we design a mechanism that updates resources and allows the dynamic entrance and exit of players over time. We sustain cooperation through a compensation scheme. Numerical results show that combining resource updates with dynamic participation increases the total payoff and strengthens the NO's incentive to invest.

cs.GT↗