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Long-term policies face a number of challenges to methodological approaches of decision-making. Decisions under deep uncertainty and complexity hardly fulfill the requirements of established optimization methods such as perfect foresight and information about the systems involved. In addition, in a world with a vast number of actors who dynamically interact across multiple levels established game theoretic approaches fail to provide reasonable solutions over long periods. Addressing the challenge, a diversity of methods is being developed and applied which draw on concepts of artificial intelligence, complex adaptive systems and agent-based modeling. The approaches describe a system dynamics that is based on decision rules and adaptive behavior, with optimal control and game theory as special cases. The various methodologies are specified and compared for decision-making in long-term climate policy. Adaptive decision rules of individual actors on emission reductions and technical change are a function of the expected utilities and risks for a given time horizon, extending the established approach of time-discounted optimization. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]