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

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 users. This 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 consideration. It is noteworthy that a joint effect of the two externalities on the vendor's management decisions exists. First, we analytically derive three patching strategies for the vendor: PS1 (rebates all users), PS2 (rebates only freeware users), and PS3 (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 externality. Specifically, when the intensity of the negative security externality is low, the vendor's optimal patching strategy will be PS1. However, with the increase in the negative security externality, the optimal patching strategy changes to PS2 and then to PS3, whereas the strategy spaces of PS1 and PS2 decrease in the positive network externality to zero. Nevertheless, if the strength of the positive network externality is relatively high, the vendor is better off selecting PS1 when the negative security externality is low. However, when the negative security externality is high, PS3 is optimal. Furthermore, based on optimal patching strategies, we reveal the optimal conditions required for the vendor to adopt the freemium model compared with commercial only. Of interest, we find that the vendor adopting the freemium version is also influenced by the interaction of the two externalities. Finally, through numerical experiments, we find that the vendor and social planner's interests can be aligned under certain conditions. However, this is not always the case. (C) 2021 China Science Publishing & Media Ltd. Publishing Services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.