An alternative proof of the characterization of core stability for the assignment game

Abstract

Solymosi and Raghavan (2001), characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. While their proof makes use of graph-theoretical tools, the alternative proof presented here relies on the notion of the buyer-seller exact representative, as introduced by Núñez and Rafels in 2002.