1. Introduction to Game Theory Yale Braunstein Spring 2007

15. Matrix Notation Notes: Player I's strategy A may be different from Player II's. P2 can be omitted if zero-sum game

16. Prisoner’s Dilemma & Other famous games A sample of other games: Marriage Disarmament (my generals are more irrational than yours)

17. Prisoner’s Dilemma 10 , 10 Blame Don't Blame Don't 20 , 0 0 , 20 1 , 1 Prisoner 1 Prisoner 2 Notes: Higher payoffs (longer sentences) are bad. Non-cooperative equilibrium  Joint maximum Institutionalized “solutions” (a la criminal organizations, KSM) NCE Jt. max.

22. Plan ahead and look back Strategy 2 Strategy 1 150 1000 25 Strategy 1 Strategy 2 - 10 You Opponent

23. If you have a dominating strategy, use it Strategy 2 Strategy 1 150 1000 25 Strategy 1 Strategy 2 - 10 You Opponent Use strategy 1

24. Eliminate any dominated strategy Strategy 2 Strategy 1 150 1000 25 Strategy 1 Strategy 2 - 10 You Opponent Strategy 3 -15 160 Eliminate strategy 2 as it’s dominated by strategy 1

27. Maximin & Minimax Equilibrium Strategies Strategy 2 Strategy 1 150 1000 25 Strategy 1 Strategy 2 - 10 You Opponent Strategy 3 -15 160 Min 1000 150 - 10 -15 160 Max

29. Is this a Nash Equilibrium? Strategy 2 Strategy 1 150 1000 25 Strategy 1 Strategy 2 - 10 You Opponent Strategy 3 -15 160 Min 1000 150 - 10 -15 160 Max

30. Cost to press button = 2 units When button is pressed, food given = 10 units Boxed Pigs Example

31. 5 , 1 Press Wait Press Wait 9 , -1 4 , 4 0 , 0 Little Pig Big Pig Decisions, decisions...

33. Mixed Strategy Safe 2 Safe 1 $ 0 $10,000 $100,000 Safe 1 Safe 2 $ 0

34. Mixed Strategy Solution

35. The Payoff Matrix for Holmes & Moriarity Player #1 Player #2 Strategy #1 Strategy #2 Strategy #1 Strategy #2 Payoff (1,1) Payoff (1,2) Payoff (2,1) Payoff (2,2) Canterbury Canterbury Dover Dover 0 100 50 0 Holmes Moriarty

37. Hawk / Dove Game

39. Hawk Dove Hawk Dove 2 2 10 0 10 0 -5 -5

41. Hawk Dove Hawk Dove 2 2 10 0 10 0 -5 -5