Adrian and Yvonne are playing a version of the ‘Ultimatum game’ in which there is a total amount of $10 to be divided between them. Adrian gets to move first and offer an amount to Yvonne of either...

Adrian and Yvonne are playing a version of the ‘Ultimatum game’ in which there is a total amount of $10 to be divided between them. Adrian gets to move first and offer an amount to Yvonne of either $0, $5, or $10. Yvonne then must decide whether to accept or reject the offer. If she accepts, then she receives the amount Adrian has offered and Adrian receives whatever is left over from $10. (For example, if he offers Yvonne $5 and she accepts, they both receive $5.) If she rejects the offer, then both Yvonne and Adrian receive zero. Assume that if Yvonne is indifferent about accepting or rejecting an offer, she will accept the offer. a Draw the game tree for this game. b Find the roll-back equilibrium of the game. Now suppose that another stage is added to the game. Suppose that if Yvonne rejects Adrian’s first offer, he gets to make another offer, but his second offer cannot be the same as the first offer. For example, if his first offer was $0 and this was rejected by Yvonne, then his second offer can only be either $5 or $10. Once Adrian makes a second offer, Yvonne again gets to choose whether to accept or reject the offer. If she accepts, then she receives the amount Adrian has offered minus $1, and Adrian receives the difference between his offer and $10 minus $1. For example, if Adrian offers $5 and it is accepted, then both Adrian and Yvonne receive $4. If Yvonne rejects Adrian’s offer, then they both receive a pay-off of $1. c Draw the game tree for this game. d Find the roll-back equilibrium of the game. e Explain why the division of the $10 in the roll-back equilibrium of the two-stage game is different from that of the one-stage version.