Suppose that you are attempting to buy a house, and you are bargaining with the current owner over the price. The house is of value $200,000 to you and $100,000 to the current owner; so if the price is between $100,000 and $200,000 then you would both be better off with the sale. Assume that bargaining takes place with alternating offers and that each stage of bargaining (an offer and a response) takes a full day to complete. If agreement is not reached after ten days of bargaining, then the opportunity for the sale disappears (you will have no house and the current owner has to keep the house forever).
Suppose that you and the current owner discount the future according to the discount factor d per day. The real estate agent has allowed you to decide whether you will make the first offer. a. Suppose that d is small; in particular d v 1 2 9 (which means that d9>1/2). Should you make the first offer or let the current owner make the first offer? Why?