1. Project BEST
Game Theory

2. Game Theory – Overview The study of strategic decision-making
Reduces “games” to mathematical objects
Games can be serious
Useful in biology, economics, politics, and computer science
Example:

3. Prisoner’s Dilemma – Description
Two isolated prisoners being questioned
Each must choose whether to reveal the other’s guilt (“defect”) or remain silent (“cooperate”)
Prison time based on
cooperation or defection
Payoff matrix
Player A
Cooperate
Defect
Player B
-3 0
0 -3

4. Prisoner’s Dilemma – Discussion
What’s the Nash Equilibrium?
Why does this present a dilemma?
Think about the Cold War – how is it related?

5. Simultaneous Move Game – Description
Five to ten players
Each player writes down their name and a number on a piece of paper
Papers will be collected and numbers averaged
Player with number closest to half of average number wins
For example, if the numbers are 57, 34, 89, 12, 64, and 73, the average is , so half is 27.4, so 34 wins

6. Simultaneous Move Game – Discussion
How did the winning number and half the average change over time?
What guided your guesses?
What would be the Nash Equilibrium for this game?

7. Sequential Move Game – Description
Break into pairs
Each pair has 21 beans
Take turns, with each player removing between 1 and 3 beans from the group
Whoever takes the last bean wins
Play three times

8. Sequential Move Game – Discussion
Did you come up with a strategy?
How quickly did you learn?
The solution
Backward induction

9. Game Theory – Applications
Stock Market
Buying a Car
Environment – for next time!
Other ideas?