In the underpriced housing market, each site is sold to an applicant who wins a lottery. Potential buyers have to select a lot maximizing their expected utility level taking into account the subjective probability to win the lottery. A logarithmic form of the subjective probability function best explains the housing lot choice behavior among four models compared. This suggests that potential buyers optimistically overestimate the winning probability. This form is of particular interest, for it mathematically coincides with logit models except for the hypethesized error term distribution.
