#### Problem Set 5

Handed out: Monday, Dec. 4

Due back: Wednesday, Dec. 13

#### Problem 5.1 Neural Nets (30 pts)

Do Problem 19.1 in the Russell-Norvig text.

#### Problem 5.2 Line Drawing Interpretation (25 pts)

Do Problem 24.2 in the Russell-Norvig text.

#### Problem 5.3 Game Theory (45 pts)

5.3.1 A Zero-Sum Game (25 pts)

Consider the following zero-sum game matrix for two players, RED and BLUE. Each player has three strategies from which to choose (strategies "A", "B", and "C"). Here is the game matrix; the values shown are the payoff for RED (the payoff for BLUE is just the negative of these values).

| BLUE-A |
BLUE-B | BLUE-C |

RED-A | -0.5 |
0.3 | 0.6 |

RED-B | 0 |
1 | 1.2 |

RED-C | 1 |
0.75 | 0.9 |

Eliminate, if possible, any dominated choices for either player; then calculate the value of this game for RED, allowing for the possibility of mixed strategies.

5.3.2 A Non-Zero-Sum Game (20 pts)

Consider the following non-zero-sum matrix for two players, BONNIE and CLYDE. Each player has two strategic choices ("A" and "B"). The game matrix is shown with CLYDE's payoff in italics:

| *CLYDE-A* |
*CLYDE-B* |

BONNIE-A | 3 | *3* | 0 | *6* |

BONNIE-B | 4 | *2* | 2 | *1* |

(a) Is this game a prisoner's dilemma situation? Why or why not?

(b) Does the game have an equilibrium point? Why or why not?