Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 20

Refer to the Ultimatum Game in Figure. Recall that the payoffs are monetary payoffs.
a. Suppose that players only care about monetary payoffs, with $1 - 1 util. Find the subgame-perfect equilibrium.
b. Suppose that players are imperfectly altruistic. They receive 1 util for each dollar they earn but util for each dollar the other player earns. Write down the extensive form reflecting the new payoffs. Find the subgame-perfect equilibrium.
c. Suppose that players are perfectly altruistic, receiving 1 util for each dollar in the sum of their earnings. Write down the extensive form reflecting the new payoffs. Find the subgame-perfect equilibrium.
d. Suppose that players are perfectly selfless, getting 1 util for each dollar the other player earns but no utility for their own earnings. Write down the extensive form reflecting the new payoffs. Find the subgame-perfect equilibrium. Does player 1 end up choosing the outcome that player 2 prefers?
Figure Ultima tum Game