We formulate a two-sided many-to-one abstract matching problem defined by a collection of agreement functions. We then propose a blind matching algorithm (BLMA) to solve the problem. Our solution concept is a modified notion of pairwise stability whereby no pair of agents can e-improve their aspiration levels. We show that the random and decentralized process of BLMA converges to e-pairwise stable solutions with probability one. Next, we consider the application of BLMA in the resource and power allocation problem of device-to-device (D2D) links underlaying a cellular network. Only one resource block (RB) can be assigned to a given D2D while D2D links may occupy many RBs at any given time. We cast the D2D allocation problem within our many-to-one matching problem. We then consider a specific instance of BLMA with limited information exchange so that agents know nothing about the value, utility, of their mutual offers. Offers are simply declared and then either accepted or rejected. Despite the market and information decentralization characteristic of the BLMA, we show that agreement of aspiration levels can still be ascertained and that attaining e-pairwise stability is feasible. Numerical results further demonstrate the convergence properties of the BLMA and that the total utility attained by the BLMA is almost equal to the total utility attained by a centralized controller.