Write down the modified version of the "divide the dollar" game in which player 2 can make a counteroffer if she does not accept player l's offer. After player 2 makes her counterofferif she doesplayer 1 can accept or reject the counteroffer. As before, if there is no agreement after the two rounds of offers, neither player gets anything. If there is an agreement in either round then each player gets the amount agreed to.
Consider the following variant of the "divide the dollar" game. Players 1 and 2 move simultaneously; 1 makes an offer to 2 and 2 specifies what would be an acceptable offer. For instance, player 1 might make an offer of 50 cents and player 2 might simultaneously set 25 cents as an acceptable offer. If player 1's offer is at least as large as what is acceptable to player 2, then we will say that there is an agreement and player 1
will pay player 2 the amount of his offer. Alternatively, if player l's offer is smaller than what player 2 specifies as acceptable, there is no agreement, in which case neither player gets anything. Draw the game tree for this game.