This paper describes ways that the definition of an equilibrium among players' strategies in a game can be sharpened by invoking additional criteria derived from decision theory. Refinements of John Nash's 1950 definition aim primarily to distinguish equilibria in which implicit commitments are credible due to incentives. One group of refinements requires sequential rationality as the game progresses. Another ensures credibility by considering perturbed games in which every contingency occurs with positive probability, which has the further advantage of excluding weakly dominated strategies.