Can data from discrete choice experiments be used to predict models be used to predict willingnes to pay by specific individuals? I am not an econometrician, but noticed that discrete choice experiments are often used to determine willingness to pay for products with specific characteristics and prices. However, these average prices seem to be reported for the average person in that sample, not being specific to specific groups of individuals. For example, by looking at the results I can't tell how that willingness to pay for a given product/price combination varies across individuals with a different socio-economic background, gender, education, etc.

Getting more specific: what would prevent one from taking a reasonably large dataset with a discrete choice experiment and develop a machine lerning model to predict willingness to pay for individuals with specific characteristics?
In principle it would be possible to do so. In fact this is exactly what we do if we convert a marginal effect at the mean to a willingness to pay. We calculate it for the average person in the dataset.

One can also distinguish the average WTP by subgroups and socio-economic characteristics such as gender. The reason why academic papers do not often go beyond that (I guess) is that the predictions become so specific that they are hardly interesting anymore. Who would be interested in the willingness to pay of say "a 27 year old male with 12 years of education, an annual income of 24000€, voting republican and an interest in violent video games"? What about when he is 28 years old? Given that these models are typically non-linear their WTPs are going to be different. 

Moving to a practical point of view price discrimination at such detailed level is impossible at the moment and for a number of products it may even be illegal (insurance is an exception).

Finally, a problem with any contingent valuation problem is that is willingness to say rather than willingness to pay. This is less of a problem in markets for goods with which the participants have experience with the good in question, but there will always be a bit of hypothetical bias.