sn- lecture 6
TRANSCRIPT
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Strategic InteractionStrategic Interaction
BLOCK 3
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To understand
The essentials of Rational Strategic Thinking
AIM Block 3
Some basic concepts and notation of Game Theory
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Rational Strategic Thinking
Lecture 6
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To discuss
Some of the most relevant ideas about strategic interaction
AIM Lecture 6
To learnHow does the logic of solving games works
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PracticalThe Grading Game
Choose between two options (X or Y). Think of this as a grading bid. You will be paired with another participant. Depending on both your choices you will get:
if (X,Y) - Grade: A, C
if (X,X) - Grade: B-, B-
if (Y,X) - Grade: C, A
if (Y,Y) - Grade: B+, B+
What would you choose?
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Tables are easier than text to observe
B- A
C B+
X
Y
X Y
Me
My pair
My grades
Grading Game
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Tables are easier than text to observe
B- A
C B+
X
Y
X Y
Me
My pair
My grades
B- C
A B+
X
Y
X Y
Me
My pair
Her grades
Grading Game
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Grading Game
Both grades in the same table
B- , B- A , C
C , A B+ , B+
X
Y
X Y
Me
My pair
Our grades
Rows
Columns
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How many chose X?
Tell Me
How many chose Y?
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How many chose X?
Tell Me
How many chose Y?
Why?
Why?
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However
This is not a game
B- , B- A , C
C , A B+ , B+
X
Y
X Y
Me
My pair
Our grades
Players
Actions they will take
Outcomes
We have:
What are we missing?
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Objectives Goals
What people care about
If we don’t know what people care about, we don’t know what the payoffs are
Payoffs
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Cannot
Tell you what your payoffs (goals, etc) should be
Strategic Interaction
But
Once we know what your payoffs are it can help you get there
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Think about differences in preferences
Self-Regarding: I only care about my grades
Other-Regarding: I also care about others’ grades
Preferences?
Let’s study the game from both of these perspectives
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Possible Payoffs
0,0 3,-1
-1,3 1,1
X
Y
X Y
Me
My pair
Our grades
Numbers represent utiles
What people are trying to achieve
Link to the outcome matrix(A,C) -> 3
(B-,B-) -> 0
What is the interpretation of this payoffs?
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Possible Payoffs
0,0 3,-1
-1,3 1,1
X
Y
X Y
Me
My pair
Our grades
People here prefer A over B+
B+ over B-
and B- over C
Self-Regarding Preferences
What should you do then?
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Whatever my pair does, I receive a higher payoff from choosing X
Definition:
It Doesn’t matter
0,0 3,-1
-1,3 1,1
X
Y
X Y
Me
My pair
Our grades
We say that my strategy X strictly dominates my strategy Y, if my payoff from X is strictly greater than that from Y. Regardless of what others do.
Rule 1: Do not play the strictly dominated strategy
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We both choose X and end up with bad payoffs (0,0)
We return to a previous point
By following rule 1
0,0 3,-1
-1,3 1,1
X
Y
X Y
Rule 2: Rational choice can lead to outcomes that are inefficient (socially)
Prisoner’s Dilemma
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Possible Payoffs 2
0,0 -1,-3
-3,-1 1,1
X
Y
X Y
Me
My pair
Our grades
Moral consciousness: Guilt (4)(A,C) -> 3 - 4=-1
(C, A) -> -1-2=-3
Other-Regarding Preferences: Conditional Cooperator
Moral Indignation: (-2)
What would you Choose?
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Not Clear
0,0 -1,-3
-3,-1 1,1
X
Y
X Y
Me
My pair
If my pair chooses X - I should choose X
If my pair chooses Y - I should choose Y
There are no strictly dominated strategies
Rule 2:
Payoffs matter
If we change them, we might get a different outcome
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Possible Payoffs 3
0,0 3,-3
-1,-1 1,1
X
Y
X Y
Me
My pair
SO FAR: Game played between people with same preferences
Mix-Match (Heterogeneity)
You are self-regarding (row)
Your pair is other-regarding
Imagine
By combining previous payoffs we can put these together
What would you Choose?
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Mix Match
0,0 3,-3
-1,-1 1,1
X
Y
X Y
Nothing has changed for the row player
X dominates Y
You should have chosen X
Now, lets change things around
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Suppose Now
0,0 -1,-1
-3,3 1,1
X
Y
X Y
Me
My pair
You are other-regarding (row)
Your pair is self-regarding
What would you Choose?
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Suppose Now
0,0 -1,-1
-3,3 1,1
X
Y
X Y
Does my X dominates my Y?
Why?
X is better against X
Y is better against Y
You should have chosen X
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No dominant for me
0,0 -1,-1
-3,3 1,1
X
Y
X Y
My X does not dominate Y
But, my pairs X dominates her Y
Rule 4: Put yourself in other’s shoes & try to figure out what they will do
Essence of Strategic Thinking
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Strategic Thinking
0,0 -1,-1
-3,3 1,1
X
Y
X Y
My X does not dominate Y
But, my pairs X dominates her Y
Rule 4: Put yourself in other’s shoes & try to figure out what they will do
Essence of Strategic Thinking
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Checklist
Do not play the strictly dominated strategy
Rational choice can lead to outcomes that are inefficient (socially)
Payoffs matter
Put yourself in the other’s shoes & try to figure out what they will do
Four Rules
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Questions?