Game theory is used in a variety of field inside and outside of social science. The standard methodology is to write down a description of the game and characterize its Nash or subgame perfect equilibria, but this is only sometimes a good approximation of observed behavior. The goal of predictive game theory is to develop models that better predict actual behavior in the field and in the lab. Core questions include: What determines people’s behavior the first time they play an unfamiliar game? When are social or altruistic preferences important, and what do people believe about other people’s social preferences? How do people update their play based on their observations? What sorts of “theories of mind,” if any, are commonly used to guide play? How do people think about games with a very large number of actions- what sort of “pruning” is involved? When will play resemble an equilibrium of the game, and which equilibrium will tend to emerge? Similarly, in a decentralized matching market, when will play converge to a stable outcome, and which one? To develop answers, researchers will need to combine insights from behavioral economics and psychology with formal modeling tools from economics and computer science