# Games in Extensive Form: Sequential Decision Making

**4.1** Introduction to Game Tree—Gambit

#### Problems

**4.1** Convert the following extensive form game to a strategic form game. Be sure to list all of the pure strategies for each player and then use the matrix to find the Nash equilibrium.

**4.1 Answer:** Player I has two pure strategies: 1 = take action 1 at node 1 : 1, and 2 = take action 2 at node 1 : 1. Player II has three pure strategies: 1 = take action 1 at information set 2 : 1, 2 = take action 2 at 2 : 1, and 3 = take action 3 at 2 : 1.

The game matrix is

There is a pure Nash at (4, 1).

**4.2** Given the game matrix draw the tree. Assume the players make their choices simultaneously. Solve the game.

**4.2 Answer:** The solution of the matrix game is the Nash equilibrium at row 2, column 1, giving payoffs (4, 0). The equivalent tree form of the game is

Matrix to tree.

Since the players make their choices simultaneously, the information set 2 : 1 reflects that player II makes her choice without ...