考虑盗版容忍度的软件产品动态定价模型

基于收益管理理论,对产品瞬态扩散模型进行拓展,选择盗版容忍度、价格和创新改进作为控制变量,扩散速度和创新水平作为状态变量,构建收益最大化的动态定价模型,依据最优化控制理论,建立哈密尔顿方程进行求解,探讨了三个控制变量的联合优化策略和相关特性,通过算例仿真验证其结论。结论显示:应采取撇脂定价策略;当由盗版引起边际收益增加的价值量与损失价值相等时,盗版容忍度达到最优;与产品生命周期的成长阶段相比较,在成熟阶段,应逐渐增加盗版容忍度,同时,减缓创新改进的速度;当损失结构降低时,应提高盗版容忍度,并且可采用创新与保护监管相互互补的策略。动态建模能够拓展静态模型中关于网络外部性的概念,分析连续状态下的变量,与自适应学习机制相一致,对实践具有更好的借鉴作用。

Dynamic Pricing Model of Software Products with Considering Piracy Tolerance

Based on the theory of revenue management, and expanding the model of transient diffusion, this paper selects piracy tolerance, price and improvement innovation as decision variables, and chooses diffuse rate and innovation level as the state variables. In accordance with the optimal control theory, the dynamic pricing model is established to maximize revenue, as well as the Hamilton Equation to discuss the joint optimization strategy and correlation properties of three control variables. By simulation calculation, the conclusion is further verified. The conclusion shows that skimming-pricing is the optimization strategy. When the increasing value of marginal revenue is equal to the loss of value caused by piracy, piracy tolerance can be optimal. Compared to the mature stage of product-life-cycle, in the growth stage, gradually increasing the piracy tolerance, and slowing down the innovation speed-improved are the best choices. With reducing the loss structure, it should improve the piracy tolerance, and adopt the mutual complementary strategies of innovation mechanism and protection. Dynamic modeling can expand the concept of network externality in static model, and analyze the variables in continuous state, it is consistent with the adaptive learning mechanism, and has a better reference for practice.