4. To discuss
Some of the most relevant ideas about strategic interaction
AIM Lecture 6
To learn
How does the logic of solving games works
5. Practical
The 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?
6. Tables are easier than text to observe
B- A
C B+
X
Y
X Y
Me
My pair
My grades
Grading Game
7. 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
8. 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
11. 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?
13. 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
14. 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
15. 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?
16. 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?
17. 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
18. 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
19. 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?
20. 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
21. 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?
22. 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
23. 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?
24. 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
25. 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
26. 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
27. 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
