Two properties of preferences and representations for choice under uncertainty which play an important role in decision theory are: (i) admissibility, the requirement that weakly dominated actions should not be chosen; and (ii) the existence of well defined conditional probabilities, that is,...

Conventional Bayesian theory of choice under uncertainty, subjective expected utility theory, fails to satisfy the properties of admissibility and existence of well-defined conditional probabilities; weakly dominated acts may be chosen, and the usual definition of conditional probabilities...

This paper develops a decision-theoretic approach to normal-form refinements of Nash equilibrium and provides characterizations of (normal-form) perfect equilibrium and proper equilibrium. The approach relies on a theory of single-person decision-making that is a non-Archimedean version of...