The basic idea of device-to-device (D2D) communication is that pairs of suitably selected wireless devices reuse the cellular spectrum to establish direct communication links, provided that the adverse effects of D2D communication on cellular users is minimized and cellular users are given a higher priority in using limited wireless resources. Despite its great potential in terms of coverage and capacity performance, implementing this new concept poses some challenges, in particular with respect to radio resource management. The main challenges arise from a strong need for distributed D2D solutions that operate in the absence of precise channel and network knowledge. In order to address this challenge, this paper studies a resource allocation problem in a single-cell wireless network with multiple D2D users sharing the available radio frequency channels with cellular users. We consider a realistic scenario where the base station (BS) is provided with strictly limited channel knowledge while D2D and cellular users have no information. We prove a lower-bound for the cellular aggregate utility in the downlink with fixed BS power, which allows for decoupling the channel allocation and D2D power control problems. An efficient graph-theoretical approach is proposed to perform the channel allocation, which offers flexibility with respect to allocation criterion (aggregate utility maximization, fairness, quality of service guarantee). We model the power control problem as a multi-agent learning game. We show that the game is an exact potential game with noisy rewards, defined on a discrete strategy set, and characterize the set of Nash equilibria. Q-learning better-reply dynamics is then used to achieve equilibrium.