Grosz & Vanoli classify combinatorial market stability with side payments

In a new paper accepted at SAGT'26, Alexander Grosz and Chiara Vanoli tackle the stability of combinatorial markets—markets where agents trade bundles of indivisible goods. Building on classic models by Bikhchandani & Ostroy and Bichler & Waldherr, they introduce explicit side payments, which allow restricted utility transfers among subsets of agents. This addition captures forms of financial collusion and generates a large number of seemingly distinct market settings. Through systematic classification, the authors uncover surprising equivalences: higher-order settings (those with more personalized prices) collapse into equivalent classes when side payments are permitted between buyers, and a similar collapse occurs for third- and higher-order settings when side payments are permitted between sellers. However, a fundamental structural separation exists between second- and third-order settings.

To analyze stability across these environments, Grosz and Vanoli introduce the T-core—a partition-based generalization of the classical core concepts with transferable utility (TU) and non-transferable utility (NTU). They relate stable outcomes across different market settings to appropriate stability notions and identify market instances where partially transferable utility yields either a better or any stable outcome. A striking finding is that under personalized pricing, all stability notions collapse to NTU-stability. This work provides a rigorous framework for understanding how restricted transfers and collusion affect market stability, with implications for auction design, regulatory policy, and decentralized finance.