New axioms for deferred acceptance

We study the problem of allocating a set of indivisible objects to a set of agents based on agents’ preferences over objects and objects’ “choice functions” over agents, when monetary transfers are not allowed. Following Kojima and Manea (Econometrica 78(2):633–653, 2010) and Morrill (Int J Game Theory 42(1):19–28, 2013a), this paper provides four characterizations of the agent-proposing deferred acceptance allocation rule for all acceptant substitutable choice functions. It is the only rule satisfying any one of the following groups of axioms: (1) stability, rank monotonicity; (2) non-wastefulness, top best, weak consistency, rank monotonicity; (3) non-wastefulness, strong top best, weak Maskin monotonicity; (4) non-wastefulness, strong group rationality, rank monotonicity. These results suggested that two new axioms: rank monotonicity and weak consistency, deserve further attention. They also shed light on what distinguishes the agent-proposing deferred acceptance rule from the other rules.