Mental disorders are a major source of disability, with few effective treatments. It has recently been argued that these diseases might be effectively treated by focusing on decision-making, and specifically remediating decision-making deficits that act as "ingredients" in these disorders. Prior work showed that direct electrical brain stimulation can enhance human cognitive control, and consequently decision-making. This raises a challenge of detecting cognitive control lapses directly from electrical brain activity. Here, we demonstrate approaches to overcome that challenge. We propose a novel method, referred to as maximal variance node merging (MVNM), that merges nodes within a brain region to construct informative inter-region brain networks. We employ this method to estimate functional (correlational) and effective (causal) networks using local field potentials (LFP) during a cognitive behavioral task. The effective networks computed using convergent cross mapping differentiate task engagement from background neural activity with 85% median classification accuracy. We also derive task engagement networks (TENs): networks that constitute the most discriminative inter-region connections. Subsequent graph analysis illustrates the crucial role of the dorsolateral prefrontal cortex (dlPFC) in task engagement, consistent with a widely accepted model for cognition. We also show that task engagement is linked to prefrontal cortex theta (4-8 Hz) oscillations. We, therefore, identify objective biomarkers associated with task engagement. These approaches may generalize to other cognitive functions, forming the basis of a network-based approach to detecting and rectifying decision deficits.