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This paper presents a new approach to the automated design of mechanisms that incentivize self-interested agents to maximize a global objective (such as revenue or social welfare) in equilibrium. Prior work on automated design has either been restricted to relatively simple mechanisms, or represented mechanisms as neural networks that are hard to interpret and cannot easily incorporate prior knowledge. In this paper, we propose program synthesis as a way around these issues. Concretely, we formalize the problem of designing mechanisms in the form of multiagent environments whose transition and reward functions are programs in a domainspecific language (DSL), in order to maximize an outcome such as revenue or social welfare under given assumptions on how agents act in these environments. We present an initial algorithm, based on a combination of stochastic search over programs and Bayesian optimization, for this problem. We empirically evaluate the algorithm in two domains with different characteristics. Our experiments suggest that the approach can synthesize programmatic mechanisms that are human-interpretable and also perform well.