Assignment Problem: Player A and B have agreed to negotiate over the division of a dollar between them. The first day, Player A will make an offer, Player B either accepts or comes back with a counteroffer the next day, and the game goes on for an indefinite period. Also assume that if a player is indifferent between two offers, s/he will accept the one that is most preferred by his/her opponent.
i) What is the sub-game perfect Nash equilibrium if there is no discounting?
ii) What is the sub-game perfect Nash equilibrium if both players have same discount rate?
iii) What is the sub-game perfect Nash equilibrium if each player has a different discount rate?
iv) Which values of discount rates ensures the maximum payoff to Player A?