On a multiple priorities matching system with heterogeneous delay sensitive individuals

•We study on the two-stage equilibrium strategies of heterogeneous delay sensitive individuals in matching systems. The non-atomic continuous and atomic discrete types of customers are discussed respectively.•We apply the sequential approach to characterize the two-stage equilibrium of such matching system specifically.•The study demonstrates that the delay sensitivities of incoming ones and balking ones at equilibrium are separated by a certain threshold.•We find that the higher the fundamental payment, the more additional fees each incoming customer is willing to pay, except for the least delay-sensitive customers.•The particle swarm algorithm is applied to obtain the optimal social benefit, along with the optimal combination of admission fees. In this paper, we study the equilibrium strategies of heterogeneous delay sensitive individuals in matching systems. Take customers as the research object. The priorities hinge on the magnitude of customers’ admission fee. Before entering the system where there are no servers, customers will make a two-stage strategy. First, customers should determine an optimal additional fee to pursue the optimal utilities, i.e., the so-called additional payment strategy. Then, they decide whether to join or not. We primarily give some necessary conditions for the equilibrium. As regards the heterogeneity of customers in delay sensitivity, both of the non-atomic continuous and atomic discrete types of customers are discussed, respectively. Applying the sequential approach, we capture the unique equilibrium for both cases. Specially, for the non-atomic continuous type of customers, the incoming ones adopt the pure additional payment strategy at equilibrium. While for the atomic discrete type of customers, the equilibrium additional payment strategies for incoming ones become mixed-type. It is found that the equilibrium additional fee and flexible cost for each incoming customer are both decreasing in fundamental payment. Finally, we use the particle swarm algorithm to consider the optimal social revenue when the incoming ones from both sides are strategic.