  Principal-Agent (PA) problems describe a broad class of economic
relationships characterized by misaligned incentives and asymmetric
information. The Principal's problem is to find optimal incentives given the
available information, e.g., a manager setting optimal wages for its employees.
Whereas the Principal is often assumed rational, comparatively little is known
about solutions when the Principal is boundedly rational, especially in the
sequential setting, with multiple Agents, and with multiple information
channels. Here, we develop RIRL, a deep reinforcement learning framework that
solves such complex PA problems with a rationally inattentive Principal. Such a
Principal incurs a cost for paying attention to information, which can model
forms of bounded rationality. We use RIRL to analyze rich economic phenomena in
manager-employee relationships. In the single-step setting, 1) RIRL yields
wages that are consistent with theoretical predictions; and 2) non-zero
attention costs lead to simpler but less profitable wage structures, and
increased Agent welfare. In a sequential setting with multiple Agents, RIRL
shows opposing consequences of the Principal's inattention to different
information channels: 1) inattention to Agents' outputs closes wage gaps based
on ability differences; and 2) inattention to Agents' efforts induces a social
dilemma dynamic in which Agents work harder, but essentially for free.
Moreover, RIRL reveals non-trivial relationships between the Principal's
inattention and Agent types, e.g., if Agents are prone to sub-optimal effort
choices, payment schedules are more sensitive to the Principal's attention
cost. As such, RIRL can reveal novel economic relationships and enables
progress towards understanding the effects of bounded rationality in dynamic
settings.
