How to have renters bid (or suggest) a rental amount?

[Bob H.]

I recently advertised a home in Colorado at what I thought was a reasonable rent. Not really. I was deluged by prospects, and I raised the rent by $100 after I had started advertising. Even with that, I received inquiries from more than 60 sets of people.

Next, I advertised a home in Oklahoma, and the response was similar. I raised the rent $50 after I had started advertising, and still I received more than 50 inquiries.

I leased both of these homes to people moving from out of town, neither of whom was in the house before leasing.

I am buying another property in Oklahoma next month. Making matters a bit more complicated, there are no homes for rent in the immediate area, either on Zillow or Realtor. Since I underestimated the market on the two other homes, I am thinking about having a "sneak preview" listing with the description inviting people to suggest a rent. I don't want to call it an auction, because I don't want to set a deadline and I don't want to feel obligated to rent to the person who offers the most rent, regardless of other qualifications.

Do you have any experience with this kind of listing or suggestions on how to create one?