A note on extended stable sets

Abstract

We study abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied for this extended relation. We formulate a characterization of stable sets for this relation and an existence theorem. Finally, we discuss its relation with Von Neumann–Morgenstern stable sets and generalized stable sets.