Playing It Safe: Consider the following dynamic game: Player 1 can choose to play it safe (denote this choice by S), in which case both he and player 2 get a payoff of 3 each, or he can risk playing a game with player 2 (denote this choice by R). If he chooses R then they play the following simultaneous-move game:
a. Draw a game tree that represents this game. How many proper subgames does it have?
b. Are there other game trees that would work? Explain briefly.
c. Construct the matrix representation of the normal form of this dynamic game.
d. Find all the Nash and subgame-perfect equilibria of the dynamic game.