Initially we prove the nonemptiness of the core of an n-person game without side payments called a central assignment game. Next, we provide a market model with indivisible goods but without the transferable utility assumption. Applying the ﬁrst result to the market model, we prove the nonemptiness of the core and the existence of a competitive equilibrium. Finally, we provide a generalization of the market model and also show the nonemptiness of the core and the existence of a competitive equilibrium using the results in the previous model.
Kaneko, Mamoru, "The Central Assignment Game and the Assignment Markets" (1980). Cowles Foundation Discussion Papers. 799.