Game theory and decision theory have a symbiotic relationship. Game theory motivates revisions in principles of rational choice. And decision theory motivates revisions in accounts of solutions to games. My project is to revise game theory in light of reflections on rational choice. I provide a new account of equilibrium in games – equilibrium among strategic reasonersmotivated by equilibrium's connection with solutions and rational choice.

To explain equilibria and solutions, let us examine a game of Hide and Seek with a time limit. The Seeker has to find the Hider before time expires; otherwise the Hider wins. The Hider can conceal herself on either the first or the second floor of a house. The second floor is smaller than the first so that the Seeker can search all of it before time expires, whereas he can search only half the first floor in the time available. The second floor has windows from which, looking down through skylights, parts of the first floor can be seen. As a result, half the first floor can be searched while searching the second floor. The players know about the windows but do not know which parts of the first floor are visible from the second floor.

Shuttling between floors would be time wasting for the Seeker. His only effective strategies are (1) searching the first floor and (2) searching the second floor. The Hider also has to choose between the first and second floors.