With the rapid advancement of sensing technologies, cloud computing, and communication systems, interaction between physical sensors and cloud-based applications has become more seamless and intelligent. This technological convergence has given rise to the concept of the Sensor-Cloud, a hybrid architecture that tightly integrates wireless sensor networks with scalable cloud infrastructures. One of the core challenges in Sensor-Cloud systems lies in efficiently managing resource allocation and task scheduling between sensors and cloud-hosted applications. Ensuring that sensors are assigned to appropriate tasks while maintaining network efficiency, fairness in resource distribution, and minimizing communication overhead remains a complex optimization problem. Traditional methods for resource management, such as heuristic algorithms and mathematical optimization techniques, often face significant trade-offs: they may offer good solutions but at the cost of high computational complexity, or achieve faster execution while compromising accuracy and fairness. To address these limitations, this paper introduces a novel game theory-based approach for resource allocation within Sensor-Cloud infrastructures. In the proposed model, each sensor acts as an autonomous rational agent that strategically selects an application to serve, aiming to maximize its own utility while contributing to overall system efficiency. By formulating this interaction as a non-cooperative game, the system dynamics naturally evolve toward a Nash equilibrium, where no sensor has an incentive to unilaterally change its allocation decision. This equilibrium represents an optimal and stable allocation of resources that balances efficiency, fairness, and computational cost. The simulation results demonstrate that the proposed method is near optimal.