In this paper we study how norms of symmetry and centricity affect the functioning of two ways to allocate resources described in the economic anthropology literature, namely reciprocity and redistribution. The baseline reciprocity study, with no explicit priming of the norm of symmetry, features near-zero levels of allocative efficiency. Consistent with the anthropological framework we use throughout, we find that priming the norm of symmetry among the players through pre-play communication dramatically increases efficiency. Next we study a game of redistribution and find that in the final stages of the game allocative efficiency levels consistently approach 100%, regardless of how the chief comes to acquire centricity in the group. We conclude that reciprocity and redistribution can seldom allocate resources efficiently in the absence of norms of symmetry and centricity in the institutional design. By way of comparison, we confirm a robust finding in the experimental economics literature that a simple market exchange game achieves high efficiency, even when the traders can formulate expectations about each other’s compliance with norms.