"The Bottle Imp" is an 1891 short story by the Scottish author Robert Louis Stevenson usually found in the short story collection Island Nights' Entertainments. It was first published in the New York Herald (February-March 1891) and Black and White London (March-April 1891). In it, the protagonist buys a bottle with an imp inside that grants wishes. However, the bottle is cursed; if the holder dies bearing it, his or her soul is forfeit to hell.

Of course, there is a catch. The bottle must be sold, for cash, at a loss, i.e. for less than its owner originally paid, and cannot be thrown or given away, or else it will magically return to him. All of these rules must be explained by each seller to each purchaser. If an owner of the bottle dies without having sold it in the prescribed manner, that person's soul will burn for eternity in hell.

(a) Assuming that the smallest possible unit of currency is a cent and that prices cannot be negative, propose a game that represents the sale of the bottle to successive owners. (b) Analyze the game using backward induction. (c) Would you buy the bottle if it were offered to you for $1 000? If your answer is not consistent with the backward induction analysis, explain your reasoning.