Serial Top Trading Cycles and the Exclusion Core in Mixed-Ownership Object Allocation Problems

2026-10-02

AI Summary

This study addresses the challenges of characterizing, testing, and analyzing stability in the exclusion core for object allocation with mixed ownership. It proposes an algorithmic framework grounded in graph-theoretic modeling via serial top trading cycles. The work establishes mixed ownership as the maximal characterizable domain and constructs fixed-point stability criteria independent of priority orderings, with formal proofs derived from game-theoretic stable set theory. Its primary contributions include a complete characterization of the exclusion core structure, demonstrating the existence of dynamic exclusion-blocking paths leading to the core, proving its von Neumann–Morgenstern stable set property, and verifying that arbitrary initial endowments converge to the exclusion core. Collectively, these results provide a unified theoretical framework for this domain.

Abstract

We study Balbuzanov and Kotowski's (2019) exclusion core for object allocation problems with complex endowments. We focus on mixed-ownership object allocation problems in which each object is either individually owned by one agent or publicly owned by all agents. Given a priority order over agents, an endowment structure, an initial allocation, and agents'preferences, we construct serial top trading cycles (STTC) graphs and define the associated STTC algorithm. The algorithm is the central tool for our analysis of exclusion-core-stable allocations. First, we show that, among domains defined by restrictions on endowment structures, the mixed-ownership domain is the largest on which the STTC algorithms characterize the exclusion core. Second, we provide a simple test for exclusion core stability: an allocation is exclusion core stable if and only if it is a fixed point of the STTC algorithm initialized at that allocation, independently of the priority order. Third, we show that the exclusion core is a von Neumann--Morgenstern (1944) stable set with respect to exclusion-domination. Finally, we study a dynamic exclusion-blocking process and show that, from any allocation, there exists a self-contained exclusion-blocking path to the exclusion core.

Problem

• exclusion core
• mixed-ownership object allocation
• serial top trading cycles
• stable set
• exclusion-blocking process

Innovation

• Serial Top Trading Cycles
• Exclusion Core
• Mixed-Ownership Object Allocation
• Stable Set
• Dynamic Exclusion-Blocking