The first key to understanding this is to recognise that consumers have preferences not over goods, but over states of the world. A "state" is a complete description of all factors that are relevant to a decision.
For example,
- in a simple consumption problem where the consumer must choose between eating a banana and an apple two states of the world would be "I have a banana" and "I have an apple". Here the preferences over states collapse back to simple preferences over goods so we see that simple preferences defined over bundles of goods are really just a special case of the more general idea of preferences over states of the world.
- Slightly more complicated: suppose you are deciding whether to take an umbrella to work. Now it's not sufficient to simply compare "I have an umbrella" with "I don't have an umbrella" because which of these I prefer will depend upon the weather! So the relevant states are something like "I have an umbrella and rain is forecast", "I don't have an umbrella and rain is forecast", "I have an umbrella and rain is not forecast", and "I don't have an umbrella and rain is not forecast".
Once we think of preferences as being over states rather than goods then it becomes easy to incorporate the kinds of dynamic elements you refer to. For example, if I am choosing between watching a movie in the cinema today versus buying a blu-ray that is released tomorrow then the states could, in principle be quite complicated:
- "I spend time travelling in the rain to the cinema where I get to see the movie early on a large screen but there may be stupid kids making noise."
- "I buy the blu-ray, which means I have to wait until tomorrow to see the movie on a small television. But I won't get wet, can watch the movie more than once, and can send my kids away to their grandmothers so they don't make noise."
This example is a bit silly, but should make clear that the idea of a state is very general and allows us to define preferences over all sorts of very exotic decision problems, including those where new goods are arriving or are becoming unavailable. indeed, the choices don't even have to be about goods that I consumer, since states of the world could be things like "I spend an extra hour in bed" vs "I go early to the park with my children".
Completeness requires that the consumer can rank all of the relevant states of the world, where a state is relevant if it could potentially be chosen by the consumer. This is obviously a big ask because there are typically a large number of factors affecting a decision problem, so the number of states a consumer must consider is large.
In practice, consumers use heuristics and approximations to solve their decision problems; they, of course, do not solve the formal, fully-specified optimisation problem. This modelling approach is, nevertheless, useful if it offers a good approximation of consumer behaviour while also making a good trade-off between tractability and empirical relevance. In fact, models of consumer demand and choice based on this simple framework typically do quite well at explaining behaviour, suggesting that this particular modelling simplification is quite useful.
The field of behavioural economics deals with situations in which consumers systematically deviate from this optimal decision process, including cases where they do not consider the full set of states.
Edit: by no means definitive, but this article by Eliaz and Spiegler (2011) is a nice example of modelling consumers who are boundedly rational and do not consider all possible states. The title and abstract are as follows:
Consideration Sets and Competitive Marketing
We study a market model in which competing firms use costly marketing devices to influence the set of alternatives which consumers perceive as relevant. Consumers in our model are boundedly rational in the sense that they have an imperfect perception of what is relevant to their decision problem. They apply well-defined preferences to a “consideration set”, which is a function of the marketing devices employed by the firms. We examine the implications of this behavioural model in the context of a competitive market model, particularly on industry profits, vertical product differentiation, the use of marketing devices, and consumers' conversion rates.
