I did not know Shubik's auction game thanks to @Gugg for putting a reference. It seems pretty interesting though. However, I think some distinctions should be made, counter-intuitive with respect to what? wrto game theoretical (in particular Nash equilibrium) predictions or wrto our predictions..
If we consider Nash equilibrium predictions, one can refer to bunch of experiments where the predictions are far from the choices of the people. For example, a recent paper is Arad and Rubinstein's 11-20 money request game. Each of two player chooses an integer amount between 11 and 20. Each player receives his/her amount. Plus a player gets 20 if s/he requests exactly one less than the other. While vast majority of people chose between 17,18 or 19, the Nash equilibrium prediction is far from it. However, I would not say this is against our intuition, besides this can be explained with another phenomenon (level-k reasoning). Basically people do not make very high-level resoning, in this case it is 3.
You know each solution concept has its assumptions, and they usually produce more than one equilibrium. I think this is one of the toughest challenge of game theory that finding a solution concept which does not produce counter-intuitive results.
Okay then that would be a tough question :). I can suggest you one another auction which describes this situation. There are actually 3 types. They are called lowest unique bid, highest unique bid and Penny auctions. Here is the link to wiki. In those type of auctions, auctioneer makes a good profit. First of all, bidders buy some chips, say 1 chip=1 Euro. Using those chips they can place a bid for an expensive phone, but each bid increases the price 1 cent! Eventually the highest bidder wins the object (usually 5€) and winner pays for it. Although it seems the price is very cheap for a phone, auctioneer receives much much more from the other bidders.