The Ultimatum game Allen and Rick need to divide $100 between them as follows: first Allen suggests an integer x between 0 and 100 (which is the amount of money he wants for himself). Rick, on hearing the suggested amount, decides whether to accept or reject.
If Rick accepts, the payoff of the game is (x, 1 - x): Allen receives x dollars, and Rick receives 100 - x dollars. If Rick chooses to reject, neither player receives any money.
(a) Describe this situation as an extensive-form game.
(b) What is the set of pure strategies each player has?
(c) Show that any result (a, 100 - a), a ∈ {0, 1,..., 100}, is a Nash equilibrium payoff. What are the corresponding equilibrium strategies?
(d) Find all the subgame perfect equilibria of this game.