Recent studies in the spatial prisoner’s dilemma embedded with a reinforcement learning framework have shown that, in a static environment, agents can learn to cooperate through a
diverse sort of mechanisms, including noise injection [1], different types of learning algorithms and neighbours’ payoff knowledge [2]. In this work, using a Q-learning algorithm for each agent, we study the effects of free space with two different types of rewards, one selfish and one
shared. We also analyze for both cases how cooperation is affected with mobility, connecting with previous results on the classical, non-reinforcement learning spatial prisoner’s dilemma [3].

Keywords
Prisoner’s Dilemma, Reinforcement Learning, Game Theory, Machine Learning

References
[1] Lu Wang, Danyang Jia, Long Zhang, Peican Zhu, Matjaž Perc, Lei Shi, and Zhen Wang.
Lévy noise promotes cooperation in the prisoner’s dilemma game with reinforcement learning.
Nonlinear Dynamics, 108(2):1837–1845, 2022.
[2] Zhengzhi Yang, Lei Zheng, Matjaž Perc, and Yumeng Li. Interaction state q-learning promotes
cooperation in the spatial prisoner’s dilemma game. Applied Mathematics and Computation,
463:128364, 2024.
[3] Mendeli H Vainstein, Ana TC Silva, and Jeferson J Arenzon. Does mobility decrease coopera-
tion? Journal of theoretical biology, 244(4):722–728, 2007