Observation, Measurement, and Computation in Finite Games

Limitations in agents’ ability to observe, measure and compute are studied. A formulation in terms of induced changes in the players’ subjective perception of the game makes it possible to study these phenomena on a common footing with objective variation in the game. We study a model where payoffs undergo continuous variation and players reason about the process from limited local information. Specifically, finite games, and statements about them, are interpreted within sheaf models, which incorporate both variation and a logic of limited observation. Nash’s theorem on the existence of equilibrium is not valid unless special observational properties hold, although closely related statements are valid. The possibility of learning to play a mixed strategy Nash equilibrium from observation of past play is also examined within the framework. Copyright Springer-Verlag 2004