@Elfryc, I should be very careful to mix in our modern notions on migration, including its politics, into a discussion about the place of migration in Ancient Cities. Whether or not Sweden or Germany or Hungary choose to shut its borders to large-scale migrations in 2015, or whether or not Trump wants to extend an existing wall, has very little to do with migrations of tribes more than seven thousand years ago.
I also reject your notion that "the great wall built to keep any invader away didn’t worked ". Not to mention that the Great Wall of China worked for very effectively for centuries, millennia, at its task. That it has been superseded doesn’t prove anything. A wall is simply one brick atop another, and is useless and worthless in itself. If anything, the cultural wall set up by Qin Shi Huangdi over two thousand years ago, still stands. Whether Huns, Mongols or other invaders, they are gone, and China still stands, a unified nation and culture, apart from any nomads or other foreign domination. Another example: while the Roman limes was manned and supported, mankind thrived through the pax romana. When corruption and self-interest took over, and the emperors squabbled and wasted, so did the limes fall, and a scourge swept through much of Europe, one of the greatest disasters in the history of our civilisation. When looking at several historic examples, like when the Normans threw out Islam and Orthodox Christianity from the Mezzogiorno, or the American push westwards, practically exterminating all that was foreign, it led to everything but “progressive backwardness” or loss of “vitality”.
I’m not trying to paint a picture saying that migration is bad, and that building walls is good, but rather: migration is a very complicated concept, it can be very good, very right, and very bad, and very wrong. It completely depends on thousands of variables. The same is true of walls. No black and white. Would France have been better off if the Franks were kept out of Gaul? No Mérovée, no Clovis, no Hugues Capet? God knows quality of life and levels of technology fell with the collapse of Roman rule. How about the Visigoths in Spain? How about invasion of Islam? And then the reconquista? The expulsion of the Moors and Jews? It’s all very complicated. The US started encouraging immigration after the civil war, but then shut its gates almost completely before WWI. They didn’t really reopen till the 1970s, and seem to be closing them again now. Sweden prided itself in the 1950s with not having any ethnic problems, while in the recent Norwegian election, Sweden’s widespread ethnic problems featured heavily. It’s all endlessly complicated. So let’s not even mention politics at all, let’s keep politics far away. A bit like the recent discussion on religion: let’s not bring up stuff that are either irrelevant or might offend. Let’s keep to ancient times.
With all that said:
I agree that migration should be an important part of the game. Like you say, the Akkadians and other Semitic or even Indo-european peoples could serve as an important model, in their contacts with the Sumerians. Maybe the Sea Peoples, the Doric invasion of Greece? In older city-building games, the city is completely build on migration, since no children are born: any population increase is because more people move in from outside. That might be a overdoing it a bit, but I do believe that migrants will make up a sizeable portion of the inhabitants of our city, natural increase would be limited. Some will be of our own people, only from other sites. Others will be similar to ourselves, another branch of the tree as it were. A few will be completely foreign, in language, religion, clothing (@lotus253!) and other matters. There might be tension, or not, depending on the differences, but also the society, and the leadership (the player). If anything, imagine the richness of the market squares, the multitude of languages!
At its most basic level there should be some note in the “info card” of each tribe member, about where they were born. This already exists in Tropico, where both tourists and foreign hired educated workers may hail from all sorts of places. It has no effect on game play though. We could also connect this with “clans” and “greater family groups” or similar, by having some family tree information available, a light version of Crusader Kings. You know, to see “which line” they are a part of, a bit like the (if you would allow me to use your nationality) Spanish Borbónes are a branch of the Bourbons of Louis XIV, in turn a line of the Capets of Saint Louis (IX), in turn a line of the Robertians of Hugues Capet. The ancient Romans of higher rank would use three names, sometimes even more, to denote their own personal name, the name of the immediate family, but also the name of the extended family, the “clan” if you will. Maybe some of our villagers, mindful of their origins, would have something similar? “Ugga-bugga, son of Og, of the Hoktoks”? 
I’m assuming that when we start, all of the the tribe members we start with would be of the same clan, the same extended family. I’m guessing then that the player would be… associated with that group? That the player, although not a person walking around in the game, would “be” a part of that clan? The original clan? And any other clan encountered in the game, let alone tribe or people, would be different, apart, foreign? Or… maybe the player has no clan, no loyalty but to the city, meaning… clans may come and go, even tribes, peoples…? Kind of like a “ruler of Paris” would start out with, maybe, some Celtic tribe, the Parisii, on a little island in the river, which in time become Latin speaking Gallic Romans of Lutetia, who are then conquered by the Franks and slowly become French in Paris? Both options would be fun…
I must though say that I am a bit hesitant regarding the role of migration and trade when it comes to technology, as you both imply, @tschuschi and @Elfryc. We know from history that many technologies and discoveries were only made once or twice, and then slowly spread across the world, from the places where a discovery was likely, to places where a discovery would never occur (but once made, it could be used). The focus on this spreading of ideas, through either trade or migration, does though undermine any possibility for the player’s tribe to single-handedly discover agriculture, metallurgy, husbandry, domestication, and so forth. Surely, over a few generations, our tribe would both learn of discoveries and inventions from afar, as well as discover and invent on its own, just like it would surely establish its own norms and culture?
Looking forward also to using tradesmen as spies, fighting to keep competent and specialised tribe members from moving away, and fearing disease in every foreigner 
)
But remember to have seen some episodes years ago (arte)
I’ll answer in several post, just by fear that it becomes unreadable.