Knowledge, Beliefs and Game-Theoretic Solution Concepts∗

In situations of strategic interaction it is important for agents to consider not only what their rivals will do, but also what they know, what they know about what they know, and so on. Formal models of knowledge have been developed to help us keep track of these levels of knowledge. This paper provides a non-technical introduction to one of these models, and investigates its foundations. It is then shown how the model can be used to analyze gametheoretic solution concepts, in particular Nash equilibrium. Fred, a young faculty member in the Department of Economics, is up for reappointment. Two professors, Gillian and Helen, have been asked to assess his competence at research and teaching respectively. Only if he is found to be good at both will he be granted tenure. The (uninformed) faculty gossip is that he is good at teaching but bad at research. After carrying out her part of the assessment, however, Gillian finds out that he is in fact good at research. Before filing her report, she offers Helen a bet that Fred will make tenure. This looks like a good bet to Helen (assuming even odds): even if her assessment is positive, she believes on the basis of the faculty gossip that Fred is probably bad at research. They are just about to shake on it when Helen has the following thought: “Gillian is about to accept the bet that Fred will make tenure. But he’ll only make tenure if his research is good. Since Gillian has assessed his research, she must know that it is good.” From the fact that Gillian is willing to accept the bet, Helen infers that Gillian knows Fred’s research is good, and the bet may not be such a good deal after all. But what if Helen’s assessment reveals that Fred is actually bad at teaching? Now she is on to a sure thing if she accepts the bet, since Fred will be granted tenure only if he is good at research ∗I am grateful to Meg Gleason and an anonymous referee for helpful comments. †Department of Economics, University of Oxford, Manor Road, Oxford, OX1 3UQ.