Two-tier marketplace with multi-resource bidding and strategic pricing for multi-QoS services

Fog computing introduces a new dimension to the network edge by pooling diverse resources (e.g., processing power, memory, and bandwidth). However, allocating resources from heterogeneous fog nodes often faces limited capacity. To overcome these limitations, integrating fog nodes with cloud resources is crucial, ensuring that Service Providers (SPs) have adequate resources to deliver their services efficiently. In this paper, we propose a game-theoretic model to describe the competition among non-cooperative SPs as they bid for resources from both fog and cloud environments, managed by an Infrastructure Provider (InP), to offer paid services to their end-users. In our game model, each SP bids for the resources it requires, determining its willingness to pay based on its specific service demands and quality requirements. Resource allocation prioritizes the fog environment, which offers local access with lower latency but limited capacity. When fog resources are insufficient, the remaining demand is fulfilled by cloud resources, which provide virtually unlimited capacity. However, this approach has a weakness in that some SPs may struggle to fully utilize the resources allocated in the Nash equilibrium-balanced cloud solution. Specifically, under a nondiscriminatory pricing scheme, the Nash equilibrium may enable certain SPs to acquire more resources, granting them a significant advantage in utilizing fog resources. This leads to unfairness among SPs competing for fog resources. To address this issue, we propose a price differentiation mechanism among SPs to ensure a fair allocation of resources at the Nash equilibrium in the fog environment. We establish the existence and uniqueness of the Nash equilibrium and analyze its key properties. The effectiveness of the proposed model is validated through simulations using Amazon EC2 instances, where we investigate the impact of various parameters on market equilibrium. The results show that SPs may experience profit reductions as they invest to attract end-users and enhance their quality of service QoS. Furthermore, unequal access to resources can lead to an imbalance in competition, negatively affecting the fairness of resource distribution. The results demonstrate that the proposed model is coherent and that it offers valuable information on the allocation of resources, pricing strategies, and QoS management in cloud- and fog-based environments.