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In the Internet of Things (IoT) + Fog + Cloud architecture, with the unprecedented growth of IoT devices, one of the challenging issues that needs to be tackled is to allocate Fog service providers (FSPs) to IoT devices, especially in a game-theoretic environment. Here, the issue of allocation of FSPs to the IoT devices is sifted with game-theoretic idea so that utility maximizing agents may be benign. In this scenario, we have multiple IoT devices and multiple FSPs, and the IoT devices give preference ordering over the subset of FSPs. Given such a scenario, the goal is to allocate at most one FSP to each of the IoT devices. We propose mechanisms based on the theory of <i>mechanism design without money</i> to allocate FSPs to the IoT devices. The proposed mechanisms have been designed in a flexible manner to address the long and short duration access of the FSPs to the IoT devices. For analytical results, we have proved the economic robustness, and probabilistic analyses have been carried out for allocation of IoT devices to the FSPs. In simulation, mechanism efficiency is laid out under different scenarios with an implementation in Python.