Two players 1 and 2 are playing a game sequentially. Player 1 moves first, and choose one of two actions: C and D. If Player 1 chooses D, the game terminates; Player 1 gets $2 and Player 2 gets $0. If Player 1 chooses C, the game continues. Player 2 observe Player 1’s action C and will choose one of two actions: E and F. If Player 2 chooses F, the game terminates,Player 1 gets $3 and Player 2 gets $1. If Player 2 chooses E, the game continues. Player 1 observes Player 2’s action E and comes back to choose one of two actions: G and H. If Player 1 chooses G, the game terminates, Player 1 gets $1 and Player 2 gets $2. If Player 1 chooses H, the game also terminates, Player 1 gets $0 and Player 2 gets $0.
(a) Specify the game in a game tree.
(b) Identify the payoffs of both players conducted by backward induction.
(c) What is player 1’s strategy set? What is player 2’s strategy set?
(d) Identify a pure-strategy Nash equilibrium under which the payoffs of both players are identical to the payoffs in question (b).
(e) Find all pure-strategy Nash equilibria.