Savage games

We define and discuss Savage games, which are ordinal games of incomplete information set in L. J. Savage's framework of purely subjective uncertainty. Every Bayesian game is ordinally equivalent to a Savage game. However, Savage games are free of priors, probabilities and payoffs. Players' information and subjective attitudes toward uncertainty are encoded in the state-dependent preferences over state contingent action profiles. In the class of games we consider, player preferences satisfy versions of Savage's sure thing principle and small event continuity postulate. Savage games provide a tractable framework for studying attitudes towards uncertainty in a strategic setting. The work eschews any notion of objective randomization, convexity, monotonicity, or independence of beliefs. We provide a number of examples illustrating the usefulness of the framework, including novel results for a purely ordinal matching game that satisfies all of our assumptions and for games for which the preferences of the players admit representations from a wide class of decision-theoretic models.