Debbie and George Calvert are thinking of making an offer to purchase a house in Shaker Heights, Ohio. Both George and Debbie saw the house this morning and fell in love with it. The asking price for the house is $400,000, and it has been on the market for only one day. Their broker told them that there were more than 20 potential buyers who saw the house that day. She also added that another broker told her that an offer on the house was going to be presented by that broker this afternoon. Their broker has advised them that if they decide to make an offer on the house, they should offer very close to the asking price of $400,000. She also added that if there are competing offers on the house that are close in value, then it is common practice for the seller to ask the potential buyers to submit their final offers the following day. Trying to be objective about this decision, Debbie has decided to construct a decision tree to help her with this decision. She has assumed that the "fair market value" of the house under consideration is $400,000. She has assigned an "emotional value" of $10,000 if she and George are successful in purchasing the house. That is, whereas the fair market value of the house is $400,000, the house is worth $410,000 to Debbie and George. Thus, if they were to be successful in purchasing the house for $390,000, the value of this outcome would be $20,000. Of course, if they were not successful in purchasing the house, the value of this outcome would be simply $0. Debbie has also assigned a probability of 0.30 that they will be the only bidders on the house. Debbie has decided to consider making one of only three offers: $390,000, $400,000, or $405,000. She estimates that if they are the only bidders, the probability that an offer of $390,000 is accepted is 0.40, the probability that an offer of $400,000 is accepted is 0.60, and the probability that an offer of $405,000 is accepted is 0.90. If, however, there are other bidders, Debbie assumes that the seller will ask them to submit a final offer the following day. In such a scenario, she will then have to rethink what to do: She can withdraw her offer, submit the same offer, or increase her offer by $5,000. She feels that in the event of multiple bids, the probability that an offer of $390,000 is accepted is 0.20, the probability that an offer of $395,000 is accepted is 0.30, the probability that an offer of $400,000 is accepted is 0.50, the probability that an offer of $405,000 is accepted is 0.70, and the probability that an offer of $410,000 is accepted is 0.80.

Structure Debbie and George's problem as a decision tree. (b) Solve for Debbie and George's optimal decision strategy.