The goal of this paper is to investigate the problem how a base station (BS), facing an unknown jamming attack, should decide to allocate scarce communication resources so as to maintain fair and reliable communication for its users. In order to obtain insight into this problem, we examine a Bayesian game using α- fairness utility, which allows the problem to be treated in a universal framework involving maximizing the total user SNR and minimizing the total user delay in transmission. The solution is a maxmin strategy (i.e. it is the optimal resource allocation under expected worst conditions), and is obtained explicitly, and thereby allows for interesting properties associated with the problem to be established.