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In this paper we study the problem of stabilizing a networked control system (NCS) composed of N linear dynamical subplants and an equal number of controllers acting over a shared network. A single subplant is allowed to communicate with its controller at each time step. Emphasis is given to both guaranteeing stability of the overall system and efficiently allocating communication. We model such a task as a non-cooperative situation wherein subplants compete for accessing to the network. By exploiting mechanism design theory we design an efficient resource allocation protocol that avoids possible subplants' strategic behaviors.