They cannot, in the way you mean. Every bid goes through a single database function that takes one bid at a time, so two bids that look simultaneous are still handled one after the other.
There is no state in which both are the highest.
What actually happens
The first one in is accepted and becomes the top bid.
The second is rejected, because by the time it is looked at, the price has moved and the amount is no longer high enough. You get a message saying so, rather than a silent failure or a bid that vanishes.
The previous top bidder is told they were outbid.
So a lost race is visible. If your bid did not take, it was not swallowed — it was refused with a reason. My bid is not the highest
On a pre-bid, where two can be equal
Pre-bids are different: two people genuinely can leave the same amount before a show starts, because they are not racing.
There the tie is broken by who placed theirs first. Highest amount wins, and among equal amounts the earliest one does.
Which is a reason to leave a pre-bid early rather than at the last moment if you were going to leave one anyway.
What it means at the end of an auction
This is where people expect unfairness and there is none: the clock does not stop a bid that was in time, and a bid that lands in the final ten seconds pushes the clock back out.
So the thing you actually have to beat is not another person's reflexes — it is their willingness to go higher. The ten seconds keep being given back until one side stops. The last ten seconds
Why it can feel otherwise
Your screen is slightly behind. The price you are looking at was true a moment ago, and on a slow connection the gap is bigger. Tapping the amount the app offers is safer than typing one you read a second ago.
The app offers you the next valid bid. Use it and you cannot be beaten by arithmetic, only by somebody bidding more. How bidding works
The practical advice
Decide your ceiling before the item comes up, then bid to it without hurrying. Speed only decides who gets a particular step; the ceiling decides who gets the item.
More: why is my bid not the highest, the last ten seconds, why is the price jumping.