Amy $($Player $1)$ and Beth $($Player $2)$ have decided to dissolve a business partnership whose assets have been valued at $$100,000.$ The charter of the partnership prescribes that the senior partner, Amy, make an offer concerning the division of the assets to the junior partner, Beth. The junior partner can Accept, in which case the proposed division is implemented, or Reject, in which case the case goes to litigation.

Litigating involves a cost of $$20,000$ in legal fees for each partner and the typical verdict assigns $60\%$ of the assets to the senior partner and the remaining $40\%$ to the junior partner.

Suppose, for simplicity, that there is no uncertainty about the verdict and that there are only two possible offers that Amy can make: a $50-50$ split or a $70-30$ split.