 In Morals by Agreement Gauthier distinguishes between straightforward maximizers and constrained maximizers. A straightforward maximizer is an orthodox Bayesian who, at any given moment in time, chooses so as to maximize her expected utility given her beliefs regarding the relevant states of affairs and the choices her counterparts might make. A constrained maximizer, on the other hand, departs from orthodox Bayesian reasoning by doing her part to bring about a fair and optimal outcome if (i) she expects her counterparts to do their part in bringing about this outcome, and (ii) she benefits as a result of all following it. A constrained maximizer thus constrains her pursuit of her interests some of the time, but reverts to straightforward maximization if she expects her counterparts to act as straightforward maximizers, or if she does not stand to benefit from constraining her behavior relative to the scenario where no one constrains their behavior.