In recent years, a lively debate in neuroeconomics has focused on what appears to be a fundamental question: Is the brain a unitary or a dual system? We are still far from a consensus view. The accumulating evidence supports both sides of the debate. A reason for the difficulty in reaching a convincing solution is that we do not yet have a clear theoretical model for either position. Here I review the basic elements and potential building blocks for such theories, using sources in large measure from classical decision theory and game theory.