I learned in school that there were many competing tribes in West Africa, but they came to be dominated by the successive kingdoms of Ghani, Mali, and Songhai. This seems quite different from the model of Europe where there were several regional powers, like France and the Habsburgs, competing with one another.
Some thoughts.
The idea that Ghana, Mali and Songhai were successive forms of essentially the same large, centralized, imperial state has been increasingly challenged by historians, most forcefully by Michael Gomez in his new book African Dominion. Gomez points out that in fact, Ghana, Mali and Gao (Songhai) co-existed or overlapped and were not simply the same basic state getting bigger and more elaborate in successive cycles of growth and collapse. Think of each of them as a kind of 'core' whose imperial peripheries shifted over time, with some of those peripheries changing hands between these three core areas and several other kingdoms or empires in the region, such as the Sosso, Mossi or Jollof states of the Senegal River valley.
These states did not dominate the entirety of West Africa. Mande-speakers and their distinctive repetoire of social forms and political practices did spread westward from the sources of the Niger down the Senegal and Gambia river valleys. But this wasn't always straightforward imperial or tributary dominion--in some cases it was closer to what we might call cultural imperialism (or even more loosely, simply influence or hegemony). People who were not themselves Mande-speaking sometimes adopted some practices and ideas of influential Mande-speaking merchants, bureaucrats and soldiers that they were in contact with, sometimes so as to facilitate a better connection to states further eastward like Mali or Ghana. Toby Green's recent scholarship on Mande creolization in Atlantic Africa covers this very well. But equally there were communities throughout Senegambia and the upper Guinea coast who pointedly rejected Mande influence and maintained their own political and social traditions, even at the risk of antagonizing powerful neighbors. There were people who were close in to the core of Mali, Gao or Ghana who were equally determined to preserve their autonomy, like the Mossi, the Dogon or various Tuareg groups. And the entire region south of the northern savannas had fairly weak ties to or knowledge of the upper Niger world and had their own strong autonomous states--Akan states before the rise of Asante, Oyo and other Yoruba states, even Hausa city-states until after Songhai rose to its largest extent, were not in any sense dominated by or even much connected to Ghana, Mali, Songhai and other upper Niger states.
The region also had plenty of very small-scale societies and communities that went about their own business without being organized into strong centralized empires or kingdoms through the entirety of what might be called the "medieval" period, though many Africanists would rather not use that term as it implies literally an "in-between" (Rome and Renaissance) that doesn't really apply to West Africa.
If you're comparing this to Western Europe in its actual medieval period, for one, it is overstating the case to sum up Western Europe as entirely about large regional powers. Take a look at a map of political dominions in the Holy Roman Empire's core area if you want to appreciate just how much fragmentation there was simply in terms of territories and dynasties with a claim to them. Moreover, for much of the medieval period, the major monarchies that ostensibly ruled large territories in fact did not have much centralized control--which is why there is so much attention to the rise of absolutism and to late medieval and early modern institutional shifts that centralized power more effectively. In certain respects, the unevenness of the European map--some important linguistic/cultural distributions that did not always match either small or large claims to sovereignty, some repeated forms of rivalry and contention between major dynastic players, some "core" areas that fought over common "peripheries", is really not terribly dissimilar to the overall complexity of West Africa in the same time period.
I think the main difference in a political-territorial sense is that West Africa had a wider variety of political systems and a more complicated and shifting correspondence between those systems and linguistic/cultural practices and distributions. To some extent also, West African polities--whether empires, kingdoms, confederations, or 'acephalous' communities--were not focused on land tenure in the same way, no matter what their political system. Kings, elites, patriarchs and other powerful figures were associated in part with clearing wild or unavailable land and maintaining its usefulness and fertility for living people, rather than exclusively owning and controlling tangibly marked off land holdings in a context where many people perceived land to be scarce. I think that meant that it was possible for the relationships between different sovereignties in West Africa to be fuzzier, more fluid, more negotiable and difficult to clarify.
First off:
were many competing tribes in West Africa
Africa scholars avoid using the word "tribe" because it carries a lot of baggage with it. here is a brief explanation for why scholars prefer to use other terminology like "peoples" "ethnicities" "states" or "polities".
Anyway, to address your question.
I don't necessarily agree with the dichotomy you are drawing where medieval Europe was multipolar and West Africa was unipolar.
The earliest written sources we have in Arabic that talk about West Africa (in the late 900s) mention Ghana alongside other polities of similar size and influence like Takrur and Gao. Ghana attracted a great deal of attention then and now because of it's reputation for wealth in gold, but it was certainly not the only West African state in the 900s-1100s.
Also, we should remember that the collapse of the Ghana kingdom in the late 1100s was not immediately followed by the rise of Mali. Indeed, the founding myth of the Mali empire, the Epic of Sundiata, centers on the political conflict between Sundiata's nascent Malian state and the established power in the region, the Sooso kingdom led by king Soumaoro Kante. This tells something of the fragmented, multipolar political situation in the upper Niger valley where there were many successor states to Ghana all contending for space in the late 12th and early 13th century.
Additionally, even as Mali reached its greatest territorial extent in the mid-14th century under Mansa Musa, there still remained neighbors who retained their independence and their own kingdoms. A generation after Musa's death, the Mossi kingdom of Yatenga was powerful enough to raid Timbuktu. Ditto, Tuareg peoples on the edge of the Sahara also raided and disrupted Mali's trade connections with the Mediterranean world. Even later in the 1300s, subject kingdoms like Jolof in what is now Senegal broke away, and a revolt at the city of Gao re-established the Songhai state in 1430.
For its part, the Songhai empire at its height (from perhaps 1480-1590) engaged in what might be seen as a proxy-struggle with Bornu over influence in the Hausa city-states. Edit- I talked about this a bit here
And of course, after 1590, the whole political geography of West Africa fragments so that by 1625 the situation looks like this
So yea, from 1100 to 1600 you see alternating periods of fragmentation and centralization around expanding empires of Mali and Songhai.
And of course, we should remember that when talking about Ghana, Mali and Songhai, they had great influence in the savanna and desert edge, but that the people of the coastal rainforest to the south largely remained outside of their political control, and states/societies like Ile Ife, Igbo Ukwu, Allada, Begho interacted with Mali and Songhai, but were able to maintain their independence.
