This is something that confuses me a bit when I see my book solve game theory problems.
When solving a model's equilibrium (like a subgame perfect nash equilibrium), the book will assume that a certain situation occurs in that equilibrium. For example, in a model with some firms setting prices and some consumers who have to make a decision to buy a product, it might assume that in equilibrium, all consumers buy.
Then it proceeds to solve for the actual equilibrium, while it always uses the assumption that they all buy.
When having solved for the equilibrium, it checks that it indeed holds in this equilibrium that all consumers buy, by e.g. showing that no consumers have an incentive to not buy.
Why is this acceptable? Isn't the derivation of the equilibrium flawed because you made an unwarranted assumption?