? E XERCISE 226.1 (Nash equilibria when players may make mistakes) Consider the three-player game…

?   EXERCISE 226.1 (Nash equilibria when players may make mistakes)  Consider the

three-player game in Figure 226.2. Show that (A, A, A) is a Nash equilibrium in which no player’s action is weakly dominated. Now modify the game by assum- ing that the outcome of any player i’s choosing an action X is that X occurs   with

probability 1 − pi and the player’s other action occurs with probability pi  > 0.

2   Show that (A, A, A) is not a Nash equilibrium of the modified game when pi  1

for i = 1, 2, 3.

 

A              B                                                 A              B

A                                                                                                 A

B                                                                                                  B

A                                                                 B

 

Figure 226.2 A three-player strategic game in which each player has two actions. Player 1 chooses a row, player 2 chooses a column, and player 3 chooses a table.