Platform companies use techniques of algorithmic management to control their users. Though digital marketplaces vary in their use of these techniques, few studies have asked why. This question is theoretically consequential. Economic sociology has traditionally focused on the embedded activities of market actors to explain competitive and valuation dynamics in markets. But restrictive platforms can leave little autonomy to market actors. Whether or not the analytical focus on their interactions makes sense thus depends on how restrictive the platform is, turning (...) the question into a first order analytical concern. The paper argues that we can explain why platforms adopt more and less restrictive architectures by focusing on the design logic that informs their construction. Platforms treat markets as search algorithms that blend software computation with human interactions. If the algorithm requires actors to follow narrow scripts of behavior, the platform should become more restrictive. This depends on the need for centralized computation, the degree to which required inputs can be standardized, and the misalignment of interests between users. The paper discusses how these criteria can be mobilized to explain the architectures of four illustrative cases. (shrink)