It's only a way of thinking about it really, but it's better than my modus operandi before, which was only a way of feeling about it.

Using our recent example, I started by saying we wanted to "buy" but needed to pay less than was offered. Then they asked what we wanted to pay and I answered honestly, respecting it wouldn't be what they wanted. Then it became a game of bid-ask ping-pong, and armed with this realization, I played like a good sport (despite them seeming to get upset at times but not because of anything I specifically did).

The game previously felt offensive, but I think honest play is merely defensive. Each party is defending their final price because once it's revealed, it terminates the game, and prematurely terminating the game in your favor is rude in a thin market. It's like deciding you'll win the game and aren't seeking a tie. It's okay for a game to not arrive at a tie, but if you actually care about your opponent, you should seek a tie.

Unfortunately, it's necessary to not reveal your final price in advance of playing the game, but only because it's the surest way to make sure you aren't easily taken advantage of (in a perfectly thin market, there isn't any other information aside from the ping-pong gameplay). At the end of bid-ask ping-pong both parties are much more likely to feel sure a tie was achieved, because just like in a real game of ping-pong, no one deserves to say exactly how the game will unfold before playing.