We consider the possibility of applying game theory to analysis and modeling of neurobiological systems. Specifically, the basic properties and features of information asymmetric signal games are considered and discussed as having potential to explain diverse neurobiological phenomena at levels of biological function that include gene regulation, molecular and biochemical signaling, cellular and metabolic function, as well as neuronal action potential discharge to represent cognitive variables that may underlie memory and behavior. We begin by arguing that there is a pressing need for conceptual frameworks that can permit analysis and integration of information and explanations across the many scales of diverse levels of biological function if we are to understand cognitive functions like learning, memory, and perception. The present work focuses on systems level neuroscience organized around the connected brain regions of the entorhinal cortex and hippocampus. These areas are intensely studied in rodent subjects as model neuronal systems that undergo activity-dependent synaptic plasticity to form and represent memories and spatial knowledge used for purposeful navigation. Examples of cognition-related spatial information in the observed neuronal discharge of hippocampal place cell populations and medial entorhinal head-direction cell populations are used to illustrate possible challenges to information maximization concepts that may be natural to explain using the ideas and features of information asymmetric signaling games.