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.

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