Reflective Oracles: A Foundation for Game Theory in Artificial Intelligence

Game theory treats players as special: A description of a game contains a full, explicit enumeration of all players. This isn’t a realistic assumption for autonomous intelligent agents. In this paper, we propose a framework in which agents and their environments are both modelled as probablistic oracle machines with access to a “reflective” oracle, which is able to answer questions about the outputs of other machines with access to the same oracle. These oracles avoid diagonalization problems by answering some queries randomly. Agents make decisions by asking the oracle questions about their environment, which they model as an arbitrary oracle machines. Since agents are themselves oracle machines, the environment can contain other agents as non-distinguished subprocesses, removing the special treatment of players in the classical theory. We show that agents interacting in this way play Nash equilibria.

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