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: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 externality.Specifically,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 zero.Nevertheless,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 low.However,when the negative security externality is high,PS_(3) 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.

Net Horizontal Payments for Ecosystem Services: An Application in the Beijing-Tianjin-Hebei Region of China

Payments for ecosystem services(PES) are one kind of important tool for environmental protection, and have been widely studied by international scholars and conservationists. Based various definitions of PES from recent articles, we have outlined four principles for PES: parity, measurability, additionality and conditionality, and then have used these principles to develop a formula to calculate a standard for PES. Finding a way to use PES to achieve a win-win relationship between economic growth and environmental protection in the Beijing-Tianjin-Hebei Region(BTHR) is a key task for Chinese government. Synergetic development of BTHR has become a national strategy, like The Belt and Road Initiative. This article employed the formula we developed to calculate the net horizontal PES amounts that each provincial government within BTHR should pay. Our findings show that Beijing should have paid 10.44×10~9 Yuan(0.4% of Beijing’s GRP) and Tianjin 16.56×109 Yuan(0.93% of Tianjin’s GRP) to Hebei in 2016.