Question

QUESTION 6 Only!

4) Draw the normal-form matrix for each of the following extensive-form games 2 E 2,2 2 F3,4 2 4, 0 0 -L-I 3,2

Answer 1

Extensive form of Game This is an example of a centipede game. Player 1 mores first, and can end the game if he chooses strategy 0. Then, the outcome of the game would be (1, 1) Alternatively, he can choose strategy I, which passes the decision-making to player 2. Now, if player 2 chooses strategy 0, the game ends with a pay-off of (-1, -1). However, if player 2 chooses strategy I, the decision-making again gets passed onto player 1. If player 1, chooses strategy V, the outcome will be (4, 0). On the other hand, if he chooses strategy D, the payoff will be (3, 2). Hence, the game can be represented in normal-form a follows: Given that: sigma_2 = (1/2, 1/2) = > This means that player 2 has a probability of 1/2 of choosing either strategy I or strategy 0. u_1(IV, sigma_2) = Expected utility of player 1 if he chooses IV when player 2 has a probability of sigma_2 = 1/2 times