Ultimatum game

Suppose that player 1 has $100 to split between herself and player 2. She oers player 2 an amount between 0 and 100 and she keeps the remaining amount for herself. Player 2 observes player 1's oer and decides whether or not to accept. If player 2 accepts, each player receives their allocated amount. If player 2 rejects, each player receives zero. Let x1 represent the money allocated to player 1 and x2 the money allocated to player 2, so x1 + x2 = 100.

a) Suppose that each player seeks to maximize her monetary payos. What is the subgame perfect equilibrium?

b) Suppose that player 1 seeks to maximize her monetary payo while player 2 is spiteful. In particular,

u1(x1,x2) = x1

u2(x2,x1) = x2 1 /2x1.What is the subgame perfect equilibrium?

c) Suppose that player 1 is altruistic while player 2 cares only about her monetary payo. In particular,

u1(x1,x2) = x1 +x2

u2(x2,x1) = x2.

What is the subgame perfect equilibrium?