A Cellular Automata Approach to Donation Game

The donation game is a well-established framework for studying the emergence and evolution of cooperation in multi-agent systems. The cooperative behavior can be influenced by the environmental noise in partially observable settings and by the decision-making strategies of agents, which may incorporate not only reputation but also traits such as generosity and forgiveness. Traditional simulations often assume fully random interactions, where cooperation is tested between randomly selected agent pairs. In this paper, we investigate cooperation dynamics using the concept of Stephen Wolfram's one-dimensional binary cellular automata. This approach allows us to explore how cooperation evolves when interactions are limited to neighboring agents. We define binary cellular automata rules that conform to the donation game mechanics. Additionally, we introduce models of perceptual and action noise, along with a mutation matrix governing the probabilistic evolution of agent strategies. Our empirical results demonstrate that cooperation is significantly affected by agents' mobility and their spatial locality on the game board. These findings highlight the importance of distinguishing between entirely random multi-agent systems and those in which agents are more likely to interact with their nearest neighbors.