Humans routinely face two types of cooperation problems: How to get to a collectively good outcome given some set of preferences and structural constraints; and how to design, shape, or shove structural constraints and preferences to induce agents to make choices that bring about better collective outcomes. In the terminology of economic theory, the first is a problem of equilibrium selection given a game structure, and the second is a problem of mechanism design by a “social planner.” These two types of problems have been distinguished in and are central to a much longer tradition of political philosophy (e.g., state of nature arguments). It is fairly clear how AI can and might be constructively applied to the first type of problem, while less clear for the second type. How to think about using AI to contribute to optimal design of the terms and parameters – the rules of a game – for other agents? Put differently, could there be an AI of constitutional design?