Satisfied two-sided matching: a method considering elation and disappointment of agents

Abstract

In practical two-sided matching problems, every agent usually cares about the matching result. If the result reaches or exceeds his/her expectation, he/she will experience elation; otherwise, he/she will experience disappointment. This is the psychological behavior of agents in two-sided matching, and the satisfaction degrees to the potential matching result of agents are closely related to the psychological behavior. However, the psychological behavior of agents is missing in the existing two-sided matching methods. The purpose of this paper is to develop a method for the two-sided matching problem considering psychological behavior of agents on both sides. First, the expected preference ordinals of each agent toward opposite agents are calculated based on the uncertain preference ordinals provided by agents. Then, the preference utility function is constructed, and the expected preference ordinals are transformed into preference utility values using the preference utility function. Next, based on the disappointment theory, the modified preference utility values are determined by calculating the disappointment values and elation values of each agent to the possible matching results. Furthermore, to maximize the sum of modified preference utility values of all agents on each side, a bi-objective optimization model is constructed, and the satisfied matching result can be obtained by solving the optimization model. Finally, a numerical example is used to illustrate the use of the proposed method.