DSGTA: A Dynamic and Stochastic Game-Theoretic Allocation Model for Scalable and Efficient Resource Management in Multi-Tenant Cloud Environments

Efficient resource allocation is a central challenge in multi-tenant cloud, fog, and edge environments, where heterogeneous tenants compete for shared resources under dynamic and uncertain workloads. Static or purely heuristic methods often fail to capture strategic tenant behavior, whereas many existing game-theoretic approaches overlook stochastic demand variability, fairness, or scalability. This paper proposes a Dynamic and Stochastic Game-Theoretic Allocation (DSGTA) model that jointly models non-cooperative tenant interactions, repeated strategy adaptation, and random workload fluctuations. The framework combines a Nash-like dynamic equilibrium, achieved via a lightweight best-response update rule, with an approximate Shapley-value-based fairness mechanism that remains tractable for large tenant populations. The model is evaluated on synthetic scenarios, with a trace-driven setup built from the Google 2019 Cluster dataset, and a scalability study is conducted with up to $K=500$ heterogeneous tenants. Using a consistent set of core metrics (tenant utility, resource cost, fairness index, and SLA satisfaction rate), DSGTA is compared against a static game-theoretic allocation (SGTA) and a dynamic pricing-based allocation (DPBA). The results, supported by statistical significance tests, show that DSGTA achieves higher utility, lower average cost, improved fairness and competitive utilization across diverse strategy profiles and stochastic conditions, thereby demonstrating its practical relevance for scalable, fair, and economically efficient resource allocation in realistic multi-tenant cloud environments.