Consider the alternating offers bargaining game to divide a surplus of 100 between Alexandra and Bill. Both can make one offer to the other player starting with Alexandra. After Alexandra makes an offer, Bill can accept or reject. If accepted, the 100 are divided as proposed by Alexandra. If rejected, Bill makes an offer to Alexandra that she can accept or reject. If Alexandra accepts, the division of 100 is implemented as proposed by Bill. If Alexandra rejects, both receive nothing. Alexandra and Bill discount each round by = .95.

(a) Suppose that both players can only make integer division proposals. Characterise all subgame perfect Nash equilibria (SPNE). [15]

(b) Now suppose the bargaining protocol is changed such that i) all proposals (a, 100 a) are allowed where a is a real number with a [0,100] and ii) the deadline is set to 41 periods where one period consists of one proposal and one decision

to accept or reject. Alexandra and Bill still make alternating offers which can be accepted or rejected and Alexandra always makes the first proposal. In the unique SPNE of this game Alexandra proposes the division (57.54, 42.46) in period 0 which

Bill accepts. Suppose now the deadline is increased by 1 period

to 42 periods. What will Alexandra propose in period 0 in the unique SPNE? Explain your answer.