Bipartite matching model with dynamic arrivals and departures

In this paper,we introduce a bipartite matching model for matching markets with dynamic arrivals and departures.Different from classical models with a finite-time horizon,our model has a long-time horizon with infinite vertices.In our model,the matching goal is to maximize the ratio of matched vertices,i.e.,matched ratio.We define two types of online algorithms,i.e.,Greedy and Patient,analyze their performance with evaluation metrics of both upper bounds and competitive ratios,and conduct extensive simulations to validate our analysis.To further simulate the real situation,we extend our model with the user’s strategic behavior and prove the existence of a specific Nash equilibrium under a differentiated matching mechanism.