[JaredL]

In any 2nd price auction, it is a dominant strategy for each player to bid her value. In this case every player has a value of 500 so they all should, but it generalises as well to for example auctions for a painting (or whatever) where some value it higher than others.

Here's the argument:
Suppose you value the object at $x.

If you bid x + k there are 3 cases:
1. you lose the auction
2. you win the auction and the second price (what you have to pay) is some y < x
3. you win the auction and the second price is some y such that x < y < x+k

In case 1 you get the same payoff, zero, if you bid x - either way you lose the auction and get nothing and pay nothing. In case 2 you would get the same payoff if you had bid x. You would win the object and pay less than what you value the object at. In the third case you win the auction but must pay more than you value it at. Therefore, you would have been better off not winning the auction and hence in this case bidding x is better.

I have just shown above that bidding your value is better than bidding above your value, no matter what the other bidders do.

Similarly suppose you bid x - k. There are 3 cases here as well:
a) You win the auction - second price is some y < x - k
b) You lose the auction, highest bid is some y such that x - k < y < x
c) You lose the auction, highest bid is some y > x

In case a had you bid x you would have the same outcome - winning the object and paying y for it. In case b if you had bid x you would pay y < x so you would be better off (you get the object and pay less than you think it's worth). In case c you would get the same outcome if you had also bid x.

So you are better off bidding your value than anything lower.

Hence you are better off bidding your value than anything higher or lower.