In this paper we study decision making in situations where the individual's preferences are not assumed to be complete. First, we identify conditions that are necessary and sufficient for choice behavior in general domains to be consistent with maximization of a possibly incomplete preference...

Two logically distinct and permissive extensions of iterative weak dominance are introduced for games with possibly vector-valued payoffs. The first, iterative partial dominance, builds on an easy-to-check condition but may lead to solutions that do not include any (generalized) Nash equilibria....

This paper proposes a model of choice that does not assume completeness of the decision maker's preferences. The model explains in a natural way, and within a unied framework of choice when preference-incomparable options are present, four behavioural phenomena: the attraction effect, choice...

Sufficient conditions are provided for a possibly incomplete preference preorder on a topological space to be closed in the product space if and only if it has closed upper and lower contour sets. Notably, it is shown that the two properties are equivalent if the domain of the preorder is a...