Stability vs. No Justified Envy, by Romm, Roth and Shorrer

 Here's a recent paper that clarifies some of the prior literature on comparing stability in two-sided matching with a related kind of envy-freeness in allocations of goods to individuals using priorities.

Romm, Assaf, Alvin E. Roth, and Ran I. Shorrer, "Stability vs. No Justified Envy," Games and Economic Behavior, Volume 148, November 2024, Pages 357-366  https://doi.org/10.1016/j.geb.2024.10.002
 
Abstract: Stability and “no justified envy” are used almost synonymously in the matching theory literature. However, they are conceptually different and have logically separate properties. We generalize the definition of justified envy to environments with arbitrary school preferences, feasibility constraints, and contracts, and show that stable allocations may admit justified envy. When choice functions are substitutable, the outcome of the deferred acceptance algorithm is both stable and admits no justified envy.