We introduce competing cognitive resilient network (CCRN) of mobile radios challenged to optimize data throughput and networking efficiency under dynamic spectrum access and adversarial threats (e.g., jamming). Unlike the conventional approaches, CCRN features both communicator and jamming nodes in a friendly coalition to take joint actions against hostile networking entities. In particular, this paper showcases hypothetical blue force and red force CCRNs and their competition for open spectrum resources. We present state-agnostic and stateful solution approaches based on the decision theoretic framework. The state-agnostic approach builds on multiarmed bandit to develop an optimal strategy that enables the exploratory-exploitative actions from sequential sampling of channel rewards. The stateful approach makes an explicit model of states and actions from an underlying Markov decision process and uses multiagent Q-learning to compute optimal node actions. We provide a theoretical framework for CCRN and propose new algorithms for both approaches. Simulation results indicate that the proposed algorithms outperform some of the most important algorithms known to date.