What type of government existed during the middle ages?

Feudalism is the right answer.

Explanation: In medieval era, before the birth of modern nation-state system, feudalism was the only form of government used to rule people. People belonging from upper nobility such as Kings or High ranked military officers were allowed to rule over people. He was the lord of people and their land.

nothing certain is known about what happened, but it seems that the country declined gradually, perhaps due to bad government, or, more likely, due to a series of bad harvests, which resulted in widespread and recurrent famine.

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