Assignment markets that are uniquely determined by their core

作者：Javier Martinez de Albeniz F; Nunez Marina^*; Rafels Carles

来源：European Journal of Operational Research, 2011, 212(3): 529-534.

DOI：10.1016/j.ejor.2011.02.024

• Cooperative games
• Assignment game
• Core
• Doubly dominant diagonal

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces a, units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core and poses the question of when the matrix is uniquely determined by the core of the related market. We characterize these matrices in terms of a strong form of the doubly dominant diagonal property. A matching between buyers and sellers is optimal if it produces the maximum units of utility. Our characterization allows us to show that the number of optimal matchings in markets uniquely characterized by their core is a power of two.

• 出版日期2011-8-1