Monotonicity and Consistency in Matching Markets

Abstract

Two-sided matchings, Maskin monotonicity, Population monotonicity, Consistency, C71, C78,

Axiomatization of the core of assignment games

“…Other forms of consistency have been proposed and the one in this paper is analogous to one offered by Nagahisa and Yamato (1992), which is called "projection consistency" by Thomson (2003). Sasaki and Toda (1992) and Toda (2003a) base a characterization of the core of marriage markets on projection consistency. (For the most comprehensive survey of consistency principle, the reader is referred to Thomson, 2003.)…”

Matching under Preferences

“…Chapter 11 (Thomson, 2015) introduces some of our matching problems within the context of fair resource allocation, namely, object allocation problems (ha), priority-augmented object allocation problems (sc), and matching agents to each other (smi and hr). The following non-exhaustive list of articles contains normative results for these problems and basic axioms of fair allocation as introduced in Chapter 11 (Thomson, 2015) (e.g., resource-monotonicity, population-monotonicity, consistency, converse consistency): Ehlers and Klaus (2004, 2011 ;Ehlers et al (2002); Ergin (2000); Kesten (2009);Sasaki and Toda (1992); Toda (2006).…”

Competition and resource sensitivity in marriage and roommate markets

“…Therefore, for marriage markets we can formulate two population monotonicity conditions that take the polarization aspect into account. The first one was introduced by Toda (2006) and we will refer to it as own-side population monotonicity: a solution ϕ is own-side population monotonic if for any marriage market (M ∪ W, R), if additional men [women] enter the market such that the new marriage market equals…”

“…Because of the polarization of interests that occurs in marriage markets, two specific versions of population monotonicity exist: own-side and other-side population monotonicity (Toda, 2006, indroduced the first of these specifications). 2 We show that in marriage markets, essentially own-side population monotonicity implies competition sensitivity (Lemma 1) and other-side population monotonicity implies resource sensitivity (Lemma 2).…”

“…One of Toda's (2006, Theorem 3.1) results can be interpreted as a corollary (Corollary 1) of our results. More importantly, Theorem 1 demonstrates that it is not really a solidarity property (population monotonicity) that is at work in Toda's (2006) characterization of the core for marriage markets, but that it is the competition sensitivity aspect that is captured as well. Our results also imply a new characterization of the core for marriage markets (Corollary 2): a solution ϕ satisfies unanimity, Maskin monotonicity, and other-side population monotonicity if and only if it equals the core.…”