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

2026-06-10

AI Summary

This study addresses the challenges of investment recovery and pricing in shared infrastructure systems, where uncertainty in revenue, heterogeneous risk preferences, and resource congestion complicate decision-making. To tackle these issues, the authors propose a risk-aware Stackelberg game in which the provider, as the leader, jointly optimizes capacity provisioning and access pricing, while users, as followers, commit to usage through take-or-pay contracts, accounting for operational costs, congestion effects, and their own risk aversion. The framework innovatively incorporates Conditional Value-at-Risk (CVaR) to model heterogeneous risk preferences, establishes the existence of equilibrium, and devises a polynomial-time approximation algorithm with provable performance guarantees. Numerical evaluations in a mobile edge computing setting reveal that higher user risk aversion leads to lower system capacity, prices, and provider profit, yet significantly improves the provider’s probability of achieving profitability.

Abstract

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms that generate revenues through resource usage. We focus on a challenging setting where: (i) infrastructure deployment requires substantial upfront investment, which the InP must recover 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. This setting is typical in emerging technologies, e.g., Mobile Edge Computing (MEC). We formalize this setting as a novel Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader and jointly optimizes capacity dimensioning and access pricing, 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 computes an approximate SE with a bounded optimality gap. We also derive a lower bound on the followers' Probability of Profit (PoP). Monte Carlo simulations for a MEC case study show that higher followers' risk aversion reduces infrastructure capacity, pricing, and leader profit, while increasing followers' PoP.

Problem

• Shared Infrastructure
• Risk Aversion
• Take-or-Pay Contracts
• Stackelberg Equilibrium
• Uncertain Revenues

Innovation

• Stackelberg equilibrium
• risk-aware contracting
• Conditional Value-at-Risk (CVaR)
• take-or-pay
• shared infrastructure