Ebay has an auto-bidding process that bids on your behalf when others bid up. In my experience, whoever was the first to bid the amount (or higher) will get the tying bid. If I bid $100, and it sticks at $90, and you bid $100, you will push the bid to $100 but I will have the top bid. Now, if I had bid $110, and you bid $100, it should still outbid you at $101 and give me the top bid. This is as fair as it can be for tying bids--first come, first serve. I have always assumed it worked this way, but it is hard to verify w/o seeing everyone else's bid.
One thing to consider is that the above algorithm means that whoever outbids you will be paying exactly as much as the second highest bidder or possibly $1-2 dollars over. The reason it can go over is to allow the bid to grow, but obviously it cannot do that if someone bids the same as you.