Came here to say this. It doesn’t even depend on knowing the other player’s value with certainty—if you shift your submitted price by $1 in your favor, you might give up a trade worth <$0.5 (if the other player’s price was between your true value and the new number), and you might improve your price by $0.5 (if a trade happens). Even if you don’t know anything for sure, it seems much more likely that a trade happens than the other player’s price being in exactly that dollar, so it’s good for you to do the price shift.
Came here to say this. It doesn’t even depend on knowing the other player’s value with certainty—if you shift your submitted price by $1 in your favor, you might give up a trade worth <$0.5 (if the other player’s price was between your true value and the new number), and you might improve your price by $0.5 (if a trade happens). Even if you don’t know anything for sure, it seems much more likely that a trade happens than the other player’s price being in exactly that dollar, so it’s good for you to do the price shift.