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gt_2007
1.
Introduction to
Game Theory Yale Braunstein Spring 2007
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
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.
18.
19.
20.
21.
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
25.
26.
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
28.
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...
32.
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
36.
37.
Hawk / Dove
Game
38.
39.
Hawk Dove Hawk
Dove 2 2 10 0 10 0 -5 -5
40.
41.
Hawk Dove Hawk
Dove 2 2 10 0 10 0 -5 -5
42.
43.
44.
45.
46.
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