In this paper, we investigate the allocation of network resources (such as FlowTable entries and bandwidth) in multi-tenant Software-Defined Networks (SDNs) that are managed by a FlowVisor. This resource allocation problem is modeled as an auction where the FlowVisor acts as the auctioneer and the network Controllers act as the bidders. The problem is analyzed by means of non-cooperative game theory, and it is shown that the auction admits a unique Nash Equilibrium (NE) under suitable conditions. Furthermore, a novel distributed learning procedure is provided that allows each Controller to reach the game’s unique NE in a few iterations by exploiting only locally available information. An implementation in OpenFlow-compliant SDNs is also proposed in a way that exploits native procedures already offered by OpenFlow. Finally, simulation results show that the proposed auction-based resource management scheme leads to significant improvements in network performance (for instance, achieving gains of up to 5 × reduction in transmission delays).