| We introduce the customer relationship management(CRM)process into the model.In this process,an enterprise aims to improve its core competitiveness and use the corresponding information and Internet technology to coordinate the interactive sales between the enterprise and customers,so as to improve the enterprise management mode and provide customers with better innovative and personalized customer interaction and service.The ultimate goal of this process is to attract new customers,maintain existing customers,and finally convert them into loyal customers,so as to increase market share.However,the conclusion of optimality is limited to the market of the model.Therefore,we define our market background and research issues as follows.We investigated a duopoly market under a mature product category,in which two competitors are committed to research the strategy of acquiring and retaining customers in order to compete for market share.These companies consider not only their own strategies to maximize their objectives,but also the actions of their competitors.Each company’s acquisition and retention services are designed to increase its own market share.A company’s acquisition behavior will reduce its competitors’ market share,while its retention behavior will make it difficult for its competitors to obtain customers.The purpose of this study is to recommend the best acquisition and retention policies for the two companies.Our analysis is carried out in a dynamic game framework,with the market share as the state variable.In our model,the two companies play Nash differential game.By using Hamilton Jacobi Bellman(HJB)equation,we get the closed-loop Nash equilibrium solution,and determine the optimal acquisition and retention expenditure to maximize customer equity.In addition,this paper also analyzes the duopoly market of service industry through sensitivity analysis and numerical examples.The results show that the optimal strategy of acquisition and retention depends on the marginal customer profit of each company,which is affected by the effectiveness of acquisition and retention.The enterprises whose acquisition effect is stronger than the retention effect are more willing to make the same investment decisions as their competitors to participate in the competition.In contrast,when the acquisition effect is lower than the retention effect,enterprises will avoid competition.In addition,we expand the model by increasing the remaining potential markets.As a oligopoly,its profit will be affected by the number of customers of competitors.Therefore,considering the interests of an enterprise,the marginal customer profit must include the marginal customer profit of the enterprise and its competitors.These two marginal customer profits together determine the optimal acquisition and retention spending strategies.We get the optimal acquisition and retention strategy by calculation,and explain the relationship between the optimal strategy and marginal customer profit. |
