Subjective Reasoning in Dynamic Games

Abstract

A unified framework is developed for representation of, and reasoning about dynamic games. A game is described by the subjective knowledge of players at hypothetical situations - the epistemic game form. Subjective knowledge - termed confidence - allows us to replace objective reasoning about hypothetical events with reasoning about the confidence of hypothetical identities, i.e., the subjective reasoning of players in hypothetical situations. This leads to an endogenous definition for players' action sets. Applying subjective reasoning to the Bear-Quiche signaling game, the Burning Money game and others, provides a characterization of the dynamic reasoning by players that leads to the suggested solutions for these games. For perfect information games, rationality and common confidence of future rationality imply backward induction, although common confidence of rationality can logically contradict the definition of the game.