An axiomatization of the nucleolus of assignment markets

Abstract

On the domain of two-sided assignment markets with agents' reservation values, the nucleolus is axiomatized as the unique solution that satisfies consistency with respect to Owen's reduced game and symmetry of maximum complaints of the two sides. As an adjunt, we obtain a geometric characterization of the nucleolus by means of a strong form of the bisection property that characterizes the intersection between the core and the kernel of a coalitional game in Maschler et al. (1979).

Evolutionary dynamics and equitable core selection in assignment games

“…3 Subsequently various authors have explored refinements of the assignment game core, including the kernel (Rochford 1984) and the nucleolus (Huberman 1980, Solymosi and Raghavan 1994, Nunez 2004, Llerena et al 2012. To the best of our knowledge, however, there has been no prior work showing how a core refinement is selected via a decentralized learning process, which is the subject of the present paper.…”

“…(See also Huberman 1980, Solymosi andRaghavan 1994. ) For an analysis of the welfare properties and of the links between the kernel and the nucleolus of the assignment game see Nunez (2004) and Llerena et al (2012).…”

Generalized three-sided assignment markets: core consistency and competitive prices

“…We need to show that x satisfies coalitional rationality and efficiency. Notice that if some side of the market is empty, the game is a two-sided assignment market and the statement follows from Proposition 2 in (Llerena et al, 2015). So, we can assume without loss of generality that M l = ∅ for all l ∈ {1, 2, 3}.…”

Insights into the Nucleolus of the Assignment Game

“…Recently Martínez-de-Albéniz et al (2013) provides a new procedure to compute the nucleolus of the assignment game. From a geometric point of view, Llerena and Núñez (2011) have characterized the nucleolus of a square assignment game, essential for our purposes. Llerena et al (2015) gives an axiomatic approach of the nucleolus of the assignment game.…”