# Warm-Up 5, Due Thursday, September 11, 12:00.

Warm-up questions usually either address material we handled during last class, or material you were to read in preparation for class, or you are supposed to answer questions based on your common sense alone. Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try to tell me why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.
Your Name:

## Question 1

Four dollar bills lie on the table. The first player, Ann, first makes an offer how to share them (like "1 for me and 3 for you", for instance), which Beth can either accept or reject. If Beth accepts, the bills are divided as agreed upon, and the game is over. If Beth rejects, two dollar bills are taken away and only two remain on the desk, and the game proceeds.

If the game proceeds, the next offer how to divide these remaining two bills is made by Beth, unless Ann gave a generous offer like "1 for Ann and 3 for Beth" or "0 for Ann and 4 for Beth" in the first round, in which case Ann has the right to do the second offer as well.

The player who didn't formulate this second offer can accept or reject. If it is accepted, the two players divide the two bills as agreed upon. If this second offer is rejected again, each player gets 50 cents, but none of the dollar bills.

How would you play as Ann, how would you play as Beth? If asked, which role would you rather want to play, Ann's or Beth's?

## Question 2

Look at the sequential game described by the following game tree (extensive form). The payoffs are the red and blue numbers at the final positions. The moves are labeled by the proposed distributions (like "1:3" or later "1:1", for instance), or by the words "accept" or "decline". Ann's possible moves and Ann's payoffs are in red, and Beth's possible moves and payoffs are in blue. How would you play as Ann, how would you play as Beth? How much money would you pay to be able to play the game as Ann? How much money would you pay to be able to play the game as Beth?