In 1954, Richard Braithwaite chose as the topic of his inaugural lecture at Cambridge The Theory of Games as a Tool for the Moral Philosopher. Braithwaite argued that by using the recently developed mathematical theory of games, philosophers could resolve certain problems in moral philosophy previously considered unsolvable. Formal game theory is a product of the twentieth century. John von Neumann and Oskar Morgenstern established game theory as an important new branch of social science with the publication of their 1944 treatise Theory of Games and Economic Behavior. However, the basic idea that motivates game theory has much older intellectual roots in the work of philosophers such as Hobbes (1651) and Hume (1740). This basic idea can be expressed in the following way: How agents behave in a given social interaction depends crucially upon their reciprocal expectations. To give an example adapted from Braithwaite’s lecture, if you and I wish to have a telephone conversation, then exactly one of us must call. I should wait for your call precisely when I expect you to call, which you should do when you expect me to wait. Even in an example this simple, issues of fairness can come into play. We both want to coordinate our behavior and have our telephone chat. But each of us may prefer to call, so as to avoid having the other pay for the call. Braithwaite used game theory to model this example, and to propose a method for assigning the roles of caller and receiver equitably. He conjectured that this method could be applied in general to problems of distributive justice.