Characterization and Computation of Equilibria for Indivisible Goods

We consider the problem of allocating indivisible goods using the leading notion of fairness in economics: the competitive equilibrium from equal incomes. Focusing on two major classes of valuations, namely perfect substitutes and perfect complements, we establish the computational properties of algorithms operating in this framework. For the class of valuations with perfect complements, our algorithm yields a surprisingly succinct characterization of instances that admit a competitive equilibrium from equal incomes.

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