The Central Assignment Game and the Assignment Markets

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Abstract
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.
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