This work addresses the fundamental problem of the trade-off between resource efficiency and user fairness in wireless networks that use opportunistic radio resource allocation. The concept of managing the trade-off by controlling the system fairness index is applied. In order to do that, two adaptive utility-based resource allocation frameworks consisting of subcarrier assignment and power allocation algorithms are proposed. These frameworks are named utility-based alpha-rule and beta-rule, and are suitable for non-real-time and real-time services, respectively. Not only can both frameworks be designed to work as wellknown classic policies found in the literature, but also as adaptive policies, which are able to meet a desired system fairness target. System level simulations show that the proposed frameworks are powerful tools to the network operator, since they can decide in which trade-off point of the efficiency-fairness plane they want to operate the system.