Achieving coordination between humans and artificial intelligence in scenarios involving previously unencountered humans remains a substantial obstacle within Zero-Shot Human-AI Coordination, which aims to develop AI agents capable of efficiently working alongside previously unknown human teammates. Traditional algorithms have aimed to collaborate with humans by optimizing fixed objectives within a population, fostering diversity in strategies and behaviors. However, these techniques may lead to learning loss and an inability to cooperate with specific strategies within the population, a phenomenon named cooperative incompatibility. To mitigate this issue, we introduce the Cooperative Open-ended LEarning (COLE) framework, which formulates open-ended objectives in cooperative games with two players using perspectives of graph theory to evaluate and pinpoint the cooperative capacity of each strategy. We put forth a practical algorithm incorporating insights from game theory and graph theory, e.g., Shapley Value and Centrality. We also show that COLE could effectively overcome the cooperative incompatibility from theoretical and empirical analysis. Subsequently, we created an online Overcooked human-AI experiment platform, the COLE platform, which enables easy customization of questionnaires, model weights, and other aspects. Utilizing the COLE platform, we enlist 130 participants for human experiments. Our findings reveal a preference for our approach over state-of-the-art methods using a variety of subjective metrics. Moreover, objective experimental outcomes in the Overcooked game environment indicate that our method surpasses existing ones when coordinating with previously unencountered AI agents and the human proxy model. Our code and demo are publicly available at https://sites.google.com/view/cole-2023.

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