Consider the following two-player game with players Ann and Beth, where Ann has three choices, A1, A2, or A3, and Beth has even four choices, B1, B2, B3, and B4.

B1 | B2 | B3 | B4 | |

A1 | 2,2 | 3,2 | 3,3 | 2,3 |

A2 | 4,1 | 3,4 | 5,2 | 4,1 |

A3 | 1,1 | 2,3 | 4,2 | 3,2 |

- (1 point) What is the payoff for Beth if Ann plays A2 and Beth plays B3?
- (1 point) Find the Maximin moves for both Ann and for Beth.
- (1 point) Which moves are strictly dominated by which moves?
- (1 point) Which moves are weakly dominated by which moves?
- (1 point) Draw the best response digraph.
- (1 point) Are there any Nash equilibria?
- (1 point) Which move do you think Ann will play? Which move do you think Beth will play? Give a reason.
- (1 point) The last question refers to the following zero-sum game:
L R U 2 1 D 3 4

- 2
- for Ann it's A2, for Beth it's B2 or B3.
- A3 is strictly dominated by A2, B1 is strictly dominated by B3.
- A3 is weakly dominated by A2, A1 is weakly dominated by A2, B4 is weakly dominated by B3, and B1 is weakly dominated by B2, B3, and B4.
- A1--->B3, A1--->B4, A2--->B2, A3--->B2, B1--->A2, B2--->A1, B2--->A2, B3--->A2, B4--->A2.
- the pair (A2, B2) is a Nash equilibrium.
- Probably Ann will play A2 and Beth will play B2. This is the Nash equilibrium, but the moves are also maximin moves.
- "R" is Beth's best response to Ann's "U", and "L" is Beth's best response to Ann's "D"

Consider the following two-player game with players Ann and Beth, where Ann has three choices, A1, A2, or A3, and Beth has even four choices, B1, B2, B3, and B4.

B1 | B2 | B3 | B4 | |

A1 | 2,2 | 3,2 | 2,3 | 3,3 |

A2 | 1,1 | 2,3 | 3,2 | 4,2 |

A3 | 4,1 | 3,4 | 4,1 | 5,2 |

- (1 point) What is the payoff for Beth if Ann plays A2 and Beth plays B3?
- (1 point) Find the Maximin moves for both Ann and for Beth.
- (1 point) Which moves are strictly dominated by which moves?
- (1 point) Which moves are weakly dominated by which moves?
- (1 point) Draw the best response digraph.
- (1 point) Are there any Nash equilibria?
- (1 point) Which move do you think Ann will play? Which move do you think Beth will play? Give a reason.
- (1 point) The last question refers to the following zero-sum game:
L R U 1 3 D 2 4

- 2
- for Ann it's A3, for Beth it's B2 or B4.
- A2 is strictly dominated by A3, B1 is strictly dominated by B4.
- A2 is weakly dominated by A3, A1 is weakly dominated by A3, B3 is weakly dominated by B4, and B1 is weakly dominated by B2, B3, and B4.
- A1--->B3, A1--->B4, A2--->B2, A3--->B2, B1--->A3, B2--->A1, B2--->A3, B3--->A3, B4--->A3.
- the pair (A3, B2) is a Nash equilibrium.
- Here it is not so clear. The Nash equilibrium pair is (A3, B2), but A3 is not the maximin move for Ann.
- "L" is Beth's best response to Ann's "U", and "L" is also Beth's best response to Ann's "D"