When we sold our house ~6 months ago we had about 7 offers and we took a solid, but middle of the pack offer in terms of price. Their offer also had strong pre-approval and financial info and they were the fastest to respond when the house went on the market. This showed us they wanted our house in particular more than the other bidders, especially considering the pre-approval for their loan and their other financial details. They were still stretching a bit to buy the house, but they came through and closed in like 3.5 weeks on a jumbo loan. Did we leave a few dollars on the table? Probably. Were we happy with the outcome, yep :)
Game theory for repeated games actually says you want to seem like a fair or generous player so that the other side doesn't defect and keeps wanting to play the game with you.