Bidding behavior given point and interval values in a second-price auction

Although rational choice theory presumes people have a point estimate of their willingness to pay (WTP) for a good or service, the idea of coherent arbitrariness suggests they have an interval of values. Herein we explore bidding behavior in a second-price auction in which bidders have point or interval values and point or interval bidding. We find bidders bid rationally: (i) when bidders have a point value but are asked to state an interval bid, they choose to bid as an interval with the point value as the mean of the interval; (ii) bidders who had a value interval but are asked to bid as a point estimate bid the expected value from the interval; and (iii) bidders with an interval value and who bid an interval such that expected bids equate expected values.