Co-Investment with Dynamic Participation under Unforeseeable Opportunity Costs: A Coalitional Game Approach

TL;DR

The paper tackles the challenge of deploying MEC infrastructure when an Infrastructure Provider (InP) and multiple Service Providers (SPs) face unforeseeable opportunity costs and benefit from sharing investment risks. It models co-investment as a transferable-utility coalitional game with dynamic participation, introducing entry fees, exit penalties, compensations, and a slack parameter to regulate participation while preserving budget balance. A convex optimization framework determines epoch-wise optimal capacity $C_k^*$ and allocations $\{h_{i,k}^{t,*}\}$, with stability ensured via core non-emptiness and a Shapley-value payoff allocation. Numerical MEC applications show the dynamic scheme outperforms static and update baselines under high opportunity costs, enabling selective participation and capacity adaption that align with demand, while highlighting the regulator-driven, transparent transfer mechanism as key to practical deployment.

Abstract

Technologies such as Mobile Edge Computing (MEC) depend on the availability of infrastructure. We define the Infrastructure Provider (InP) as the actor responsible for deploying and maintaining this infrastructure, while Service Providers (SPs) operate applications over it to serve end users and earn revenues. Deploying such infrastructure requires however a significant investment, and the InP may be reluctant to bear it alone. We propose co-investment to overcome this barrier, allowing players, the InP and multiple SPs, to share costs and revenues. However, committing to a co-investment over a long period may be too constraining for players: in an unforeseeable future, players may realize that they could make more profit outside the co-investment (such a profit is called opportunity cost). For this reason, we propose a scheme, based on coalitional game theory, which is dynamic in terms of (i)allowing players to join, remain in, or leave the co-investment, (ii) adjusting the infrastructure capacity and resource sharing over time. We propose a method to compute entry fees and exit penalties in order to appropriately compensate players remaining in the co-investment. We numerically show that our dynamic scheme encourages player participation and increases profit (in case of high opportunity cost).

Figures (8)

• Figure 1: Total payoff under different opportunity costs, with values averaged over 20 simulation runs
• Figure 2: Infrastructure capacity evolution across intervals, for the case of moderate opportunity cost, with values averaged over 20 simulation runs
• Figure 3: Per-player payoff $x_{i, k}^{\mathcal{S}_k}$ across intervals, for the case of moderate opportunity cost and for one simulation run
• Figure 4: Participation evolution across intervals, for the case of moderate opportunity cost and for the same simulation run presented in Fig. \ref{['fig:ind']}
• Figure 5: Traffic level evolution $B_{i,k}^t$ (see \ref{['eq:load_equation']}) across intervals

Theorems & Definitions (16)

• Definition 3.3
• Definition 3.5
• Proposition 3.7
• proof
• Definition 3.8
• Definition 3.9
• Proposition 3.10
• proof
• Definition 3.11
• Definition 3.14