Consider the following incomplete information variation on the Ru binstein model. Two players are bargaining over splitting $10.00. They take turns making offers, with discount factor 6 = .999999 applied every time an offer is rejected. Player 1 seeks to maximize her expeeted payoff. There is incomplete information about player 2. Player 1 assesses prob ability 7f that player 2 seeks to maximize his expected payoff, and she assesses probability 1 -7f that he will ask for $8.00 precisely every time he is able to offer, and he will resolutely turn down any offer that leaves him with less than $8.00.
(a) Construct a sequential equilibrium for this bargaining game for the case 7f = .2. (This is hard, but not impossible.)
(b) Construct a sequential equilibrium for this bargaining game for the case 7f = .8. (This is harder.)
(c) Construct a sequential equilibrium for every possible value of 7f (and, in particular, for 7f very close to one). (Good luck!)