Fairness and Nonwastefulness in Two-Period Matching

Abstract

In this paper, we explore a two-period matching problem in which agents' preferences may evolve over time. This model enables agents to be matched with different partners over the two periods. Previous research defines dynamic stability as the absence of any single agent or pair of agents gaining an advantage through coalition across any period. We introduce new fairness, nonwastefulness and individually rationality notions tailored for the two-period matching setting and examine its relationship with dynamic stability. We also discuss the existence of matching that simultaneously satisfies the newly introduced fairness and nonwastefulness properties.