We present a formal framework for distributed databases, and we study the complexity of the concurrency control problem in this framework. Our transactions are partially ordered sets of actions, as opposed to the straight-line programs of the centralized case. The concurrency control algorithm, or scheduler, is itself a distributed program. Three notions of performance of the scheduler are studied and interrelated: (1) its parallelism, (2) the computational complexity of the problems it needs to solve and (3) the cost of communication between the various parts of the scheduler. We show that the number of messages necessary and sufficient to support a given level of parallelism is equal to the minimax value of a combinatorial game. We show that this game is PSPACE-complete. It follows that, unless \(NP=PSPACE\), a scheduler cannot simultaneously minimize communication and be computationally efficient. This result, we argue, captures the quantum jump in complexity of the transition from centralized to distributed concurrency control problems.