  Solving the problem of cooperation is fundamentally important for the
creation and maintenance of functional societies. Problems of cooperation are
omnipresent within human society, with examples ranging from navigating busy
road junctions to negotiating treaties. As the use of AI becomes more pervasive
throughout society, the need for socially intelligent agents capable of
navigating these complex cooperative dilemmas is becoming increasingly evident.
Direct punishment is a ubiquitous social mechanism that has been shown to
foster the emergence of cooperation in both humans and non-humans. In the
natural world, direct punishment is often strongly coupled with partner
selection and reputation and used in conjunction with third-party punishment.
The interactions between these mechanisms could potentially enhance the
emergence of cooperation within populations. However, no previous work has
evaluated the learning dynamics and outcomes emerging from Multi-Agent
Reinforcement Learning (MARL) populations that combine these mechanisms. This
paper addresses this gap. It presents a comprehensive analysis and evaluation
of the behaviors and learning dynamics associated with direct punishment,
third-party punishment, partner selection, and reputation. Finally, we discuss
the implications of using these mechanisms on the design of cooperative AI
systems.
