In this paper, a novel strategy for the control of a string of vehicles is designed. The vehicles are coupled in a unidirectional ring at the interaction level: each vehicle is influenced by the position of its immediate forward neighbor; the first vehicle in the platoon is influenced by the position of the last vehicle. Through these interactions a cooperative behavior emerges and a platoon of vehicles moving at a constant velocity with constant inter-vehicle spacings is formed. This contrasts with more traditional control schemes where an independent leader vehicle is followed by the remaining vehicles. For this control structure, stability properties are established. The concept of string stability of a platoon is discussed and applied to the ring interconnection. Design rules are presented, showing how an appropriate choice of parameter values leads to a constant spacing or constant time headway policy. Furthermore, the scheme has a characteristic property: it maintains the platoon structure when subject to malfunctioning vehicles.