Strategic InteractionStrategic Interaction

BLOCK 3

To understand

The essentials of Rational Strategic Thinking

AIM Block 3

Some basic concepts and notation of Game Theory

Rational Strategic Thinking

Lecture 6

To discuss

Some of the most relevant ideas about strategic interaction

AIM Lecture 6

To learnHow does the logic of solving games works

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?

Tables are easier than text to observe

B- A

C B+

X

Y

X Y

Me

My pair

My grades

Grading Game

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

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

How many chose X?

Tell Me

How many chose Y?

How many chose X?

Tell Me

How many chose Y?

Why?

Why?

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?

Objectives Goals

What people care about

If we don’t know what people care about, we don’t know what the payoffs are

Payoffs

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

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

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?

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?

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

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

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?

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

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?

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

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?

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

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

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

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

Questions?