  Cooperation plays a crucial role in both nature and human society, and the
conundrum of cooperation attracts the attention from interdisciplinary
research. In this study, we investigated the evolution of cooperation in
optional prisoner's dilemma games by introducing simple bots. We focused on
one-shot and anonymous games, where the bots could be programmed to always
cooperate, always defect, never participate, or choose each action with equal
probability. Our results show that cooperative bots facilitate the emergence of
cooperation among ordinary players in both well-mixed populations and a regular
lattice under weak imitation scenarios. Introducing loner bots has no impact on
the emergence of cooperation in well-mixed populations, but it facilitates the
dominance of cooperation in regular lattices under strong imitation scenarios.
However, too many loner bots on a regular lattice inhibit the spread of
cooperation and can eventually result in a breakdown of cooperation. Our
findings emphasize the significance of bot design in promoting cooperation and
offer useful insights for encouraging cooperation in real-world scenarios.

Physics and Society