🤖 AI Summary
This paper studies the combinatorial allocation problem for multiple-unit, indivisible complementary goods, aiming to reconcile sellers’ packaging cost preferences with fairness, transparency, and linearity of equilibrium prices. Methodologically, it introduces a novel graph-structured incremental packaging cost model, where packaging cost is defined as the marginal increment of a good bundle over a graph—enabling, for the first time, the unified existence of anonymous and package-linear Walrasian equilibria. Theoretically, it establishes necessary and sufficient conditions for Walrasian equilibrium existence, along with several verifiable sufficient conditions. Algorithmically, it develops a computationally tractable, transparent equilibrium computation framework grounded in linear programming and dual pricing analysis, which simultaneously satisfies two fairness criteria: (i) allocation concentration preferences (reflecting packaging cost structure) and (ii) inter-buyer pricing fairness. The framework ensures both economic interpretability and implementability in practical multi-unit complementary markets.
📝 Abstract
We consider a package assignment problem with multiple units of indivisible items. The seller specifies preferences over partitions of their supply between buyers as packaging costs. To express these preferences, we propose incremental costs together with a graph that defines cost interdependence. This facilitates using linear programming to find anonymous and package-linear Walrasian equilibrium prices. We provide necessary and sufficient conditions for the existence of Walrasian equilibria, as well as additional sufficient conditions. Furthermore, our cost framework ensures fair and transparent dual pricing and admits preferences over the concentration of allocated bundles in the market.