Keep in mind, Mesopotamia is first and foremost a place. While there have been civilizations and empires that have risen and fallen within this region, the fact remains that Mesopotamia is not a civilization in and of itself.
This is an important factor to note, given that, in different periodizations, there would have been differing degrees of unification within the region. The Sumerians, for example, were divided into various city-states competing with one another. That being said, there were also periods where one regional power would conquer its competitors to gain hegemony over Mesopotamia (and even beyond its borders): examples include the Assyrians, originating in Northern Mesopotamia, or the Babylonians. There were also times where the entire region was invaded and conquered from outside its borders entirely: examples would include the Persians (who would later be conquered by the Macedonians under Alexander the Great).
If you look at the ancient world as a whole, monarchy tends to be the predominate form of government, and Mesopotamia is no exception. At the same time, it is also important to keep in mind the degree to which religion and monarchy tended to be intertwined with one another in the Ancient World, with rulers understood as being servants to the gods, or in some cases, even being gods themselves (the most famous example of this can be found in the Pharaohs of Ancient Egypt). Whether you are discussing periods of political fragmentation or periods of greater political unification, this same pattern tends to hold, of government being dominated by kings.