The whole population of Europe didn't travel to the Americas. In fact it was usually the poorer people in economically depressed or politically unstable areas that came. If you were relatively well off there wasn't a good reason to leave Europe unless you wanted adventure. Germans, English, Scots, and Poles in the 1700s. Irish, Jews from Eastern Europe, Southern Italians, more Germans, and Czechs in the 1800s. Japanese, Chinese, and other east Asians in the 1900s, etc.
Historically, there are two types of migrations to consider in Game Terms:
Voluntary Migration. Historically, this was usually Internal, as in people migrating to the nearest City from the countryside for jobs, access to power, protection, etc. This is already in the game in the form of City Growth, since birthrate and survival was notoriously poor in cities for most of history: the population growth in most of our game cities is actually internal migration.
The big 'external' voluntary or semi-voluntary migration has occurred in the past few hundred years, and involved primarily but not entirely migration of people to the Americas looking for jobs, land, freedom from persecution, etc. I call this 'semi-voluntary' because frequently the alternative to migration was to starve or be mobbed back home (or, in my family's case, be picked up by the local constabulary, since every ancestor we've found has been a crook of some kind and came to America one step ahead of the Law back in Europe!). So, this type of migration required both Bad Conditions back home and Open Borders and Open Land/Opportunity at the destination. There are also cases of Government-Sponsored Migration: Russia inviting Germans to settle and farm open lands under Catherine the Great, or the English forming a Ruling Class in Ireland and resulting in a distinctly 'mixed' cultural/genetic group there.
Involuntary Migration: usually, getting Pushed Out of wherever you were with catastrophic results to gather folks living wherever you are forced to go. These date back to pre-history everywhere, as in the migration of the Apache from northeastern Canada to the American Southwest, the migrations of Celts, Germans, Goths, and Hsung-Nu (Huns) in historic Europe/Asia, the Indo-European groups before them in many of the same areas. They could be caused by changes in environment and climate, although the specifics of this are hotly debated, or by the actions of other Human Groups.
In Game Terms, these would usually take the form of a bunch of Barbarian Camps being forced to relocate into or next to your borders, but there is no game mechanism for moving these Camps, nor any mechanism to put pressure on them to move.
Note. Most of the so-called Migratory Civilizations were actually Pastoral: they did not drive their herds and people into new areas unless Forced, but stayed within a single, large area which they fiercely defended. It was only when the Chinese put pressure on the Hsung-Nu that they became Migrants, and brought their herds and families into entirely new areas and into conflict with the peoples of Europe.
So the most important aspect for the Game would be how to model Pastoral Civilizations, with the potential to 'burst out' and crush their settled neighbors, or migrate and disrupt half a continent. This has been debated at length in other Threads all the way back to Civ IV at least. Suffice to say that many of the civilizations that are considered 'normal' in the game are in fact Pastoral and very badly modeled in the game because they were not city builders for most of their history: Mongols, Huns, Scythians, etc.
What makes modeling the Pastorals difficult is that, as powerful and important as they might be in the Ancient, Classical or Medieval Eras, they dwindle into insignificance after that unless they settle down and start building cities and industry. Producing a mechanism for initial Pastoral Civ is not too difficult: finding a way for that to morph into a settled Civ with cities and factories without requiring them to 'conquer' an already settled Civ (as did the Turks) is more difficult, but necessary to make the entire Pastoral/Migrant Civilization concept worthwhile in game terms. Who wants to play a Civ that you can only play for the first third of the game?
