In TPIR, people have to try and guess the price of an item, and whoever comes closest without going over wins. So if I bid after another player, I can bid one dollar more than him, effectively stealing his bid (unless he happened to guess exactly right). People do this quite frequently; it's not uncommon to see the fourth and final bidder bid one dollar higher than the highest of the three other bids.
Of course this works at the top and bottom - so you should also bid one dollar lower than the lowest if you think it is lower than everyone thought. This is all only true if you are bidding last, any time before that you should be honest* to give the later players the toughest choice of going higher or lower than you.
If you go last and think it is between two other bids you chose 1 higher than the lower bid (because of the too high bids being ignored).
*I think in fact because of the high bids rule there is always an incentive to shave your bid to err on the low side, but it is difficult to quantify what size this effect is.
