Yes it oversimplified. Suppose that a = b, i.e both companies has the same market share. Also suppose that when both companies has equal market share their innovations rates are the same, same price etc.
The model has two equilibrium both companies compete in which their market share fluctuates around a = b. and we get a sort of predator-pray model[1].
Both companies do not compete their market share stays the same.
What does it means to compete? It could mean many things like not putting lower prices, delaying innovations until competitor has release their own etc.
What does it means to compete? It could mean many things like not putting lower prices, delaying innovations until competitor has release their own etc.
[1] http://ccnmtl.columbia.edu/projects/seeu/dr/restrict/modules...