Bikhchandani and Mamer (1997, J. Econom. Theory 74, 385-413) studied an exchange economy with multiple indivisible objects and established a necessary and sufficient condition for the existence of competitive equilibrium by a linear programming approach. This paper provides an alternative proof of their theorem by the core of a coalitional form game. Journal of Economic Literature Classification Number: C71. (C) 2000 Academic Press.