Multi-agent reinforcement learning (MARL) is a powerful framework for studying emergent behavior in complex agent-based simulations. However, RL agents are often assumed to be rational and behave optimally, which does not fully reflect human behavior. Here, we study more human-like RL agents which incorporate an established model of human-irrationality, the Rational Inattention (RI) model. RI models the cost of cognitive information processing using mutual information. Our RIRL framework generalizes and is more flexible than prior work by allowing for multi-timestep dynamics and information channels with heterogeneous processing costs. We evaluate RIRL in Principal-Agent (specifically manager-employee relations) problem settings of varying complexity where RI models information asymmetry (e.g. it may be costly for the manager to observe certain information about the employees). We show that using RIRL yields a rich spectrum of new equilibrium behaviors that differ from those found under rational assumptions. For instance, some forms of a Principal's inattention can increase Agent welfare due to increased compensation, while other forms of inattention can decrease Agent welfare by encouraging extra work effort. Additionally, new strategies emerge compared to those under rationality assumptions, e.g., Agents are incentivized to increase work effort. These results suggest RIRL is a powerful tool towards building AI agents that can mimic real human behavior.