Let there be four contestants in a game similar to "The Price Is Right". They simultaneously write down bids for an object they don't know, the bids can range from 1 to 1000 USD. The object's value will be 75% of the average of the four bids. The bid nearest to the value will win, and it does not matter whether the bid is too high (unlike in The Price Is Right). Is there an optimal play?
I think there is none, because if there was, then all four contestants would bid the same amount, giving them each a chance of 25% to win. However, for every single contestant it would be advantageous to make a different bid, thus this cannot be a Nash equilibrium.
Is that correct? Or is there a different way to think about this problem?