### CSCI 3202: Artificial Intelligence, Fall 2000

#### 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?