To reap the benefits of dense small base station (SBS) deployment, innovative backhaul solutions are needed in order to manage scenarios in which high-speed ground backhaul links are either unavailable or limited in capacity. In this paper, a novel backhaul scheme that utilizes unmanned aerial vehicles (UAVs) as an on-demand flying network linking ground SBSs and the core network is proposed. The design of the aerial backhaul scheme is formulated as a network formation game among UAVs that seek to form a multi-hop backhaul network in the air. To solve this game, a myopic network formation algorithm which reaches a pairwise stable network upon convergence, is introduced. The proposed network formation algorithm enables the UAVs to form the necessary multi-hop backhaul network in a decentralized manner thus adapting the backhaul architecture to the dynamics of the network. Simulation results show that the proposed network formation algorithm achieves substantial performance gains in terms of both rate and delay reaching, respectively, up to 40% and 41% compared to the formation of direct communication links with the gateway node (for a network with 15 UAVs).