Based on two formats of books $-$ paper book and electronic book, book publishers often sell their products to online consumers through e-tailers by adopting reselling mode and agency selling mode simultaneously. This paper develops a dynamic pricing game model on basis of a long-term gradient adjustment mechanism for a book supply chain that consists of a publisher and an e-tailer, and focuses on the impacts of agency fee rate and adjustment speed on the complexity of the dynamic game. We compare the system stability and the average profits for a dynamic decentralized decision and a dynamic centralized decision. The results show that a higher agency fee rate makes the dynamic system more stable, and a higher adjustment speed makes the dynamic system become more unstable with exhibiting a period doubling bifurcation. Moreover, the dynamic decentralized system is more stable than the dynamic centralized system as the adjustment speed increases. Under the dynamic decentralized decision, the profits of the publisher and the supply chain decrease while the e-tailer's profit increases when the game system loses its stability. In addition, it is interesting to find that in a certain parameter region, the profit of the supply chain under the dynamic decentralized decision is higher than that under the dynamic centralized decision.

基于两种格式的书籍 $-$纸质书和电子书，图书发行商通常通过同时采用转售模式和代理销售模式，通过电子零售商向在线消费者出售产品。本文基于由出版商和电子零售商组成的图书供应链的长期梯度调整机制，开发了一种动态定价博弈模型，并着重研究了代理费率和调整速度对图书定价复杂性的影响。动态游戏。我们比较了动态分散决策和动态集中决策的系统稳定性和平均利润。结果表明，较高的代理费率使动态系统更加稳定，较高的调整速度使动态系统变得更加不稳定，并呈现出周期加倍。此外，随着调整速度的增加，动态分散系统比动态集中系统更加稳定。在动态分散决策下，当游戏系统失去稳定性时，发行商和供应链的利润减少，而电子零售商的利润增加。此外，有趣的是，在某个参数区域中，动态分散决策下的供应链利润要高于动态集中决策下的供应链利润。