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Studying social-ecological systems, in which agents interact with each other and their environment are important both for sustainability applications and for understanding how human cognition functions in context. In such systems, the environment shapes the agents' experience and actions, and in turn collective action of agents changes social and physical aspects of the environment. Here we review current investigation approaches, which rely on a lean design, with discrete actions and outcomes and little scope for varying environmental parameters and cognitive demands. We then introduce a multiagent reinforcement learning (MARL) approach, which builds on modern artificial intelligence techniques, and provides new avenues to model complex social worlds, while preserving more of their characteristics, and allowing them to capture a variety of social phenomena. These techniques can be fed back to the laboratory where they make it easier to design experiments in complex social situations without compromising their tractability for computational modeling. We showcase the potential MARL by discussing several recent studies that have used it, detailing the way environmental settings and cognitive constraints can lead to the emergence of complex cooperation strategies. This novel approach can help researchers bring together insights from human cognition, sustainability, and AI, to tackle real world problems of social-ecological systems.