Assignment Markets with Budget Constraints

TL;DR

This paper extends assignment market models to include hard budget constraints, proposing an iterative auction that maintains incentive compatibility and core stability under certain conditions, but highlights computational hardness otherwise.

Contribution

It introduces a demand-query-based auction for markets with budget constraints, addressing incentive compatibility and stability issues not covered in traditional models.

Findings

Proposes an iterative auction that preserves properties under a specific condition.

Shows incentive compatibility and core stability are incompatible without the condition.

Demonstrates the problem is NP-hard even with complete information.

Abstract

This paper studies markets where a set of indivisible items is sold to bidders with quasilinear, unit-demand valuations, subject to a hard budget constraint. Without financial constraints the well-known assignment market model of Shapley and Shubik (1971) allows for a simple ascending auction format that is incentive-compatible, and strongly Pareto-optimal. However, this auction model does not capture the possibility that bidders face hard budget constraints. We design an iterative auction that depends on demand queries and an easily verifiable additional condition to maintain the properties in the presence of budget constraints. If instead this additional condition does not hold, incentive compatibility and core stability are at odds, and we cannot hope to achieve strong Pareto optimality in a simple ascending auction even with truthful bidding. Moreover, even in a complete information model where the auctioneer has access to valuations and budget constraints, the problem is NP-hard.