"So your bidding against his computer that increases the price"
You are not bidding against the computer. You are bidding against another bidder who is willing to pay more than you do.
eBay keeps identity of bidders secret (a**3 for example)). It has been that way for a few years.
So, if someone bids $50 (for example) on an item with a $25 starting bid and you bid $26, the "computer" (eBay's proxy system working on behalf of the other bidder) will raise the price to $27. If you then bid $28, the proxy system will raise the bid to $29, etc... until the other bidder has reached his/her maximum bid of $50.
From eBay's help pages:
Proxy bidding
The feature of an auction-style listing in which eBay automatically bids on the buyer's behalf, up to the maximum amount they set. Enter the maximum amount you're willing to spend on an item, and eBay will continue to bid incrementally for you until either you're the high bidder or your maximum is reached. This means you don't have to keep coming back to bid every time someone else places a bid.