The figure below illustrates the tree of a strictly competitive game G of perfect information without chance moves. (a) How many pure strategies does each player have? (b) List each player’s pure strategies using the notation introduced in class. (c) What play result from the use of the pure strategy pair (rll, LM)? (d) Find all pure strategy pairs that result in the play [ rRl ]. (e) Write down the strategic form of G. (f) Find all the saddle points. (g) Apply Zermelo’s algorithm to the game: What is the value of G? What is the value of the subgame starting at node b? What is the value of the subgame starting at node c? Show that the pure strategy rrr guarantees that player I gets the value of G or better. Why is this pure strategy not selected by Zermelo’s algorithm? (h) Find all Nash equilibria of the game. Which of these are subgame-perfect?
