The goal of this project is to provide new foundations for a more robust decision theory and game theory that, among other things, does not assume that the state and outcome space are known, nor that the game is common knowledge. The proposed framework would allow for the incorporation of unanticipated observations, deal with the fact that different agents can be aware of different features of the world and the game, even to the extent that they might not be aware of all the possible moves that they can make or of which agents are playing the game, allow for the possibility that agents might use different languages to describe a decision problem or game, and allow for the fact that part of learning involves modifying the language (i.e., learning new concepts). The project will use techniques that involve viewing acts as syntactic programs and representing the (lack of) awareness of agents in a formal logic. The broader impact of the proposed work includes making decision theory and game theory more robust, and thus far more applicable in complex environments ranging from exploration of Mars by robots (where there are bound to be unanticipated events) to auctions in large peer-to-peer networks (where the identity of all the players is certainly not commonly known).
