I tried to do some research and I can expect two parts of the answer, one of wich was originally posted as a comment
I already stated:
With the increasing techno-control operated by over-the-tops and the power of big data such situation could be possible in the future. Airlines will recognize devices by ID or cookies and match them with individual profiles provided by tracking networks (advertising, marketing), and calculated with (not only) searches and social media posts of the individual and his network. A "need-to-buy" score might in the future be used to increase prices and/or deny discounts on individual basis, on the grounds that the customer is more likely to buy the product at any condition.
I said that there is little technical barrier preventing such. Defending your privacy on the web is an option, but it is out of the scope of the question (see also: How do I prevent cookies and apps to track my entire life?)
Now that I have space for that, the "need-to-buy" score is a theoretical score (I am trying to find the patent by Amazon for its real name) that a predictive market analysis may apply to an individual versus a product. The higher the score, the more the individual feels the need to buy that product and the more he is available to pay on grounds of the need. Soemthing opposite to the well-known concept of market demand which is made only on big figures. Flu example: flu vaccine can become more expensive in October because many people fall sick, hence more demand, not because you are demanding it.
On the downside, the above hypothetical approach does not work in a competitive market. Airlines operating on the same route compete each other. Assuming (by absurd) that they both know you have no choice than fly, they still want to compete each other on selling you a seat, hence a good reason to lower their price tag. Note that my illustration might look like the airline decides the price to apply by the time you browse their website with your browsing history in your cookies.
AI is not capable of that, to my knowledge. Marketing strategies are planned very well in advance on statistical models. As highlighted in other answers, the airline's pricing model may increase price on last-minute passengers because in the past years they found this strategy to generate good revenue. Marketers don't care about your loss.
I doubt it could be possible in Europe, but with an asterisk*
In Europe, there are severe non-discriminatory pricing rules, and Antitrust is very active on that.
Non-discriminatory pricing is a broad definition. It does not limit to gender/race/etc. for individuals. It is the principle that any company that is selling utility is required to apply the same price to any individual or business customer.
So an airline selling London-Warsaw for, say, an advertised price of 200€, cannot require you, @jasonPark, to pay 400€ for the same flight because they know you are in an urge. When I say they sell it for 200€ I assume I will browse their site with a "neutral" browser in incognito mode from a network that could not be easily tracked back to you: i.e. the price I would see.
The asterisk is: I can't find information whether product discounts can be discriminatory. In general, I think they can because some companies do normally make personalized voucher codes for individuals that opted in to market researches.
This is the caveat: even if they knew (assume they know), the airline cannot overprice the ticket above the maximum fare, but may refuse to propose you a discounted price.