🤖 AI Summary
This study investigates the stability of combinatorial markets when side payments are introduced, focusing on equilibrium properties under constrained utility transfers among agents. By constructing an explicit side-payment mechanism, the work proposes a partition-based notion of stability under restricted transferable utility—termed the T-core—and systematically classifies distinct market settings. Integrating combinatorial market modeling, cooperative game-theoretic core theory, and analyses of both transferable (TU) and non-transferable utility (NTU) stability, the paper uncovers key structural differences: when side payments are permitted among buyers, higher-order market formulations become equivalent; among sellers, equivalence holds only from the third order onward. Furthermore, under personalized pricing, all stability concepts collapse to NTU stability.
📝 Abstract
Combinatorial markets provide a general framework for trading bundles of indivisible goods. Building on the combinatorial market models of Bikhchandani & Ostroy (2002) and Bichler & Waldherr (2017), we introduce explicit side payments, thereby allowing restricted transfers of utility among subsets of agents and capturing different forms of financial collusion.
This extension results in a large number of seemingly distinct market settings. However, we establish a systematic classification of their expressive power. Most notably, we show that higher-order market settings (i.e., those with more personalized prices and less clearinghouse power) are essentially equivalent in terms of market properties when side payments are permitted between buyers. An analogous collapse occurs for the third- and higher-order settings when side payments are permitted between sellers. In contrast, we identify a fundamental structural separation between the second- and third-order settings.
To analyze stability in these environments, we generalize the classical concepts of stability with and without transferable utility (TU and NTU) to a partition-based notion of restricted transferability (the $T$-core). We relate stable outcomes across different settings to appropriate stability notions, identify market instances in which partially transferable utility yields a better (or any) stable outcome, and show that under personalized pricing, all stability notions collapse to NTU-stability.