Stronger core results with multidimensional prices
New research introduces multi-dimensional prices to guarantee stable allocations in markets without money.
A team of computer scientists and economists, including Mark Braverman, has published a groundbreaking paper titled 'Stronger core results with multidimensional prices' on arXiv. The work tackles a fundamental problem in market design dating back to Hylland and Zeckhauser's 1979 paper: in one-sided matching markets without money (like assigning students to schools or donors to recipients), a stable competitive equilibrium often doesn't exist, and the 'strong core' of stable allocations can be empty. This has been a persistent theoretical hurdle for designing fair and efficient allocation systems.
The researchers' key innovation is generalizing the concept of competitive equilibrium by assigning each item a multi-dimensional price instead of a single scalar value. They prove that a solution using this novel pricing scheme always exists and, crucially, that it resides within the 'rejective core'—a stability concept stronger than the traditional weak core. Furthermore, they demonstrate 'core convergence,' showing that as an economy grows large, the set of these stable allocations converges to the set of competitive equilibria with multi-dimensional prices. This provides a robust theoretical foundation for stable market design in non-monetary settings.
- Solves the 47-year-old problem from Hylland and Zeckhauser (1979) where competitive equilibria fail in markets without money.
- Introduces multi-dimensional prices, proving a solution always exists and resides in the stronger 'rejective core'.
- Demonstrates core convergence, linking the new solution concept to competitive equilibria as the economy scales.
Why It Matters
Provides a theoretical backbone for designing stable, efficient allocation systems for school placement, organ donation, and resource matching without money.