Abstract : Suppose η buyers are eyeing on η distinct houses in a locality for sale. The houses are owned by η distinct individuals who value their houses differently. The buyers too value the houses differently depending on their personal preferences. It is possible to represent the problem as a cooperative game among 2η persons where the gains from cooperation are represented by a matrix A = (aij) where i is a seller and j is a buyer. The real issue is how to split the gains of cooperation. We will introduce the notion of the core for this game and show it is no empty. We will show how to arraive at a core element via some graph theoretic ideas.