1) Two countries, A and B, are bargaining to split a total that starts out at $100. A makes the first offer, stating how the $100 will be divided between them. If B accepts the offer, the game is over. If B rejects it, the total available to bargain is reduced by $1 to $99. Then B gets to make an offer. The players take turns making offers this way, and each round the amount shrinks by $1. A makes offer in the odd numbered periods, and B makes offers in the remaining periods until they reach an agreement or they run out of money to divide. A's outside option is $2.25 and B's outside option is $3.50. Assume that if players are indifferent between an offer and their BATNA, they accept the offer. Also assume that they do not discount future payoffs. Find the sub-game perfect equilibria of this game.
Please explain whether the follow statements are true or false and explain why. Note you must explain you answer to receive full credit.
2) Bargaining involves a zero-sum interaction with conflict.
3) With complete information and no commitment problems, the occurrence of war fulfills the Nash Bargaining Solution according to Fearon (1995).
4) There are $100 on the table and two players, each of whom prefers more money to less. I tell Player 1 to propose a division of the $100 to Player 2. Player 2 then either accepts or rejects the division. If Player 2 accepts the division, both players walk away with their negotiated amounts. If not, then both players walk away with nothing. Player1's sub-game perfect nash equilibrium strategy involves her offer Player 2 $50.
5) The problem above is an example of a Nash Bargaining Solution.