ECO - Suppose you are attempting to buy a used bicycle

Suppose you are attempting to buy a used bicycle, and you are bargaining with the owner over the sale price. The bike is worth $200 to you and $100 to the owner (he can sell it to another customer at a later  date). 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 no agreement is reached after 3 days of bargaining,  then the opportunity for sale disappears and both get zero. Suppose that both you and the current owner  discount the future according to a discount factor of δ per day. The seller has allowed you to make the  first offer. (Denote the buyer as player 1, the seller as player 2, and denote the selling price by x.) 

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