Analysis of Asymmetric Two-Sided Matching: Agent-Based Simulation with Theorem-Proof Approach

This paper discusses an extended version of the matching problem which includes the mate search problem; this version is a generalization of a traditional optimization problem. The matching problem is extended to a form of the asymmetric two-sided matching problem. An agent-based simulation model is built and simulation results are presented. Todd and Miller (1999) simulated the two-sided matching problem in a symmetric setting. In his model, there are the same number of agents in both parties (groups), each of whom has his/her own mate value. Each agent in a party tries to find his/her mate in the other party, based on his/her candidate's mate value and his/her own aspiration level for his/her partner's mate value. Each agent learns his/her own mate value and adjusts his/her aspiration level through the trial period (adolescence). Todd and Miller (1999) tried several search rules and learning mechanisms that are symmetric for both parties. In the present paper, Todd and Miller's (1999) model is extended to an asymmetric setting where the two parties have different numbers of agents, and the search rule and the learning mechanism for the two parties differ. Through the simulation, the search rules and the learning mechanisms which were identified to be appropriate in a symmetric setting are revealed to be inappropriate in the asymmetric setting and the reason why this is so is discussed. Furthermore, some general facts are derived using a mathematical theorem-proof approach. Some of these facts are used to direct a revision of the model, and a revised simulation model is presented. An implication is obtained for practical situations in asymmetric matching setting. For example, in the job hunting case, if job applicants want to finish their job hunting successfully, they should be modest at the beginning of the hunt.