How did Empires respond to increased diversity and Interconnectedness?

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Your question does not specify the name of the Empires you are referring to, or the date in history. However, we can comment on these general terms.

If we take into consideration empires in 1750 CE, these empires responded to increased diversity and Interconnectedness in that they ended with former trade networks that existed and created new ones to exploit trade to their favor. We are talking about powerful empires such as the Ottoman Empire in eastern Europe and the Middle East, the Mughal Empire in India, the Safavid Empire in Southwest Asia, the Russian Empire, and the Ming Dynasty in China.