I had a vague expectation that I was supposed to do something strategic but I wasn’t sure what. (It turns out this was in fact false)
Actually, unlike a standard second price auction where it’s game theory optimal to just bid your fair value, there is a strategic element to this game, since the price you bid or offer will affect the clearing price. In this case, the price at which your P(trade_occurs) * expected_utility_gain_from_trading is maximized is probably not your true fair value. To give one simple example, if you were 100% confident their bid would be higher than your fair, you would definitely want to offer above your fair so that the mid price is higher.
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.
Actually, unlike a standard second price auction where it’s game theory optimal to just bid your fair value, there is a strategic element to this game, since the price you bid or offer will affect the clearing price. In this case, the price at which your P(trade_occurs) * expected_utility_gain_from_trading is maximized is probably not your true fair value. To give one simple example, if you were 100% confident their bid would be higher than your fair, you would definitely want to offer above your fair so that the mid price is higher.
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.