Offering coupons through the mail, online ad codes etc. You are reaching out to different demos using different marketing techniques and offering or not offering discounts accordingly.
Where? This anecdote is oft repeated with little evidence. The only I example I remember is some place getting caught doing it and having to stop because of the bad press.
"As shown in Figure 11, Travelocity alters hotel search results for users who browse from iOS devices." (In particular, alters the prices shown to the user).
I was shopping for flights last Christmas and got price X on every site. I started checking out and the price became X+50. I got angry and left and came back later to find the price, on all sites, was X+80. Since I had no choice but to travel I paid X+80. Then for kicks and self torture I checked the price on my Android phone and it was still around X.
Jacking up prices when revisiting the site from the same browser is a separate thing. It’s there to encourage you to buy ASAP as prices appear to be increasing rapidly.