Optimal adoptions of freemium version and patching strategy:Network and security externalities

作     者：Nan Feng Hanyue Zhang Changqing Dong Jie Zhang Minqiang Li Jing Xie 

作者机构：College of Management and EconomicsTianjin UniversityTianjin300072China College of Business AdministrationUniversity of Texas at ArlingtonArlingtonTX76019USA 

出 版 物：《Journal of Management Science and Engineering》 (管理科学学报（英文版）)

年 卷 期：2022年第7卷第1期

页      面：107-132页

学科分类：0839[工学-网络空间安全] 08[工学] 

基　　金：国家自然科学基金 

主　　题：Freemium Positive network externality Negative security externality Patching strategy 

摘      要：The freemium pricing model has become mainstream in the software industry.A large user base can induce positive network effects while expanding security risks associated with unpatched *** study explores a two-stage decision problem faced by software vendors that involves a freemium versioning strategy and a subsequent security-patching strategy when taking both the positive network externality and negative security externality into *** is noteworthy that a joint effect of the two externalities on the vendor’s management decisions ***,we analytically derive three patching strategies for the vendor:PS_(1)(rebates all users),PS_(2)(rebates only freeware users),and PS_(3)(rebates no users).Our results indicate that,if the strength of the positive network externality is relatively low,the optimal security-patching strategy will be significantly affected by the negative security ***,when the intensity of the negative security externality is low,the vendor’s optimal patching strategy will be PS_(1).However,with the increase in the negative security externality,the optimal patching strategy changes to PS_(2) and then to PS_(3),whereas the strategy spaces of PS_(1) and PS_(2) decrease in the positive network externality to ***,if the strength of the positive network externality is relatively high,the vendor is better off selecting PS_(1) when the negative security externality is ***,when the negative security externality is high,PS_(3) is ***,based on optimal patching strategies,we reveal the optimal conditions required for the vendor to adopt the freemium model compared with commercial *** interest,we find that the vendor adopting the freemium version is also influenced by the interaction of the two ***,through numerical experiments,we find that the vendor and social planner’s interests can be aligned under certain ***,this is not always the case.