Game Theory
A tool for modeling strategic
interactions
Parts to a Game
1. A set of players
2. A set of actions available to each player
3. A payoff function that specifies how
actions are mapped into payoffs for each
player
A Penalty Kick in Soccer
1. Players = (Kicker, Goalie)
2. Actions
for Kicker - (Kick Left, Kick Right)
for Goalie –
(Defend Kick Left, Defend Kick Right)
A Penalty Kick in Soccer
3. Payoffs – Kicker wins if Goalie guesses
wrong and looses if Goalie guesses
correctly. Goalie payoff is the opposite.
Normal Form Game
A table that graphically represents all of the parts to a game.
Normal Form Game
A table that graphically represents all of the parts to a game.
Players
Kicker
Kick Left
Kick Right
Defend Kick Left
W,L
L,W
Defend Kick Right
L,W
W,L
Goalie
Normal Form Game
A table that graphically represents all of the parts to a game.
Actions
Kicker
Kick Left
Kick Right
Defend Kick Left
W,L
L,W
Defend Kick Right
L,W
W,L
Goalie
Normal Form Game
A table that graphically represents all of the parts to a game.
Payoffs (row player’s payoff listed first)
Kicker
Kick Left
Kick Right
Defend Kick Left
W,L
L,W
Defend Kick Right
L,W
W,L
Goalie
Today’s Experiment
Get into 8 groups of 3-4 people per group.
Communication between groups is not allowed.
Your grade is based upon the number of points
that your group earns. Your points are the sum
of your payoffs from the games. For each game
you will be playing against another randomly
selected group from the class.
Game of Chicken
Other
Chicken
1
Tough
7
Chicken
4,4
2,10
Tough
10,2
0,0
You
Network Effects – Walkie Talkie
Don’t Buy
4
Buy
4
Don’t Buy
4,4
4,0
Buy
0,4
8,8
Other
You
Game of Trade
Other
Trade
No Trade
8
Trade
6,6
0,10
No Trade
10,0
4,4
You
Driving Game
Other
Left Side
Right Side
8
10,10
0,0
0,0
10,10
You
Left Side
Right Side
Cartel Game – Output Level
Other
Low
High
8
Low
8,8
5,10
High
10,5
6,6
You
Location Game
Other Little Rock Fayetteville
7
1
You
Little Rock
2,2
10,5
Fayetteville
5,10
1,1
Rock Paper Scissors
Other
You
Rock
5
Paper
1
Scissors
2
Rock
5,5
0,10
10,0
Paper
10,0
5,5
0,10
Scissors
0,10
10,0
5,5