In competitive scenarios, we analyze the optimal pricing, launch timing, and influencing factors of new products by establishing three differential game models. The findings indicate that (1) the depreciation rate of old products directly impacts the pricing strategies of advantaged and disadvantaged enterprises. Enterprises with competitive advantages tend to set higher prices for new products when old products depreciate faster, while those with fewer advantages adjust their pricing strategies by initially increasing prices for the latest prices and eventually reducing them. (2) The rate of old‐product depreciation also affects the timing of new‐product launches. Advantaged enterprises tend to delay their product launches when the impact of the new product on the old ones is significant, while disadvantaged enterprises opt for earlier launches under similar circumstances. (3) The technological level of the new product influences the timing of its launch for both advantaged and disadvantaged enterprises. Higher technological levels prompt advantaged enterprises to launch earlier and disadvantaged enterprises tend to follow suit. (4) High levels of innovation in new products by advantaged enterprises prompt earlier launches by disadvantaged enterprises. These results may offer valuable insights for enterprises in formulating effective product rollover strategies.

中文翻译：

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基于微分博弈的竞争场景产品滚动策略

在竞争场景中，我们通过建立三种差异博弈模型来分析新产品的最优定价、上市时机和影响因素。研究结果表明：（1）旧产品折旧率直接影响优势企业和劣势企业的定价策略。当旧产品贬值速度较快时，具有竞争优势的企业往往会为新产品制定较高的价格，而优势较小的企业则会调整定价策略，先针对最新价格提高价格，然后再降低价格。 (2)旧产品的折旧率也会影响新产品的推出时机。当新产品对旧产品影响较大时，优势企业往往会推迟产品上市，而劣势企业在类似情况下会选择提前上市。 (3)新产品的技术水平对优势企业和劣势企业的上市时机都有影响。技术水平越高，优势企业越早推出，劣势企业往往会跟风。 （四）优势企业新产品创新水平高，带动劣势企业先行推出新产品。这些结果可以为企业制定有效的产品更新策略提供有价值的见解。