Game Theory (Prisoners' Dilemma) | Market Structure

Delve into the intriguing concept of the prisoners' dilemma in game theory as it relates to economic decision-making. Discover how this classic scenario showcases the challenges of cooperation and competition, and the implications it has on outcomes in different contexts.

1. Game Theory: The Prisoners’
Dilemma
Economics

2. What is the Prisoners’ Dilemma?
•A situation where a player has to adopt his own strategy because he is
unsure of the other player’s courses of action.
•It shows why firms in an oligopolistic market must cooperate for the
best outcomes for all the players.

3. Why is it called the Prisoners’ Dilemma
•The name originates from a situation in which two people who
were detained on suspicion of committing a crime decided to
confess and get a longer prison sentence than they would receive, if
they had cooperated by not confessing.

4. The Prosecutors face a difficult situation
I’m not going to
confess. I don’t want
to lose 12 years of
my life.
You can’t be serious!
I won’t confess.

5. Prosecutors explore another option:
separating the suspects

6. The payoff matrix
The following payoff matrix shows the outcomes, that is, jail terms,
when two suspects, Jane and Jerry , choose to confess or not to confess.
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Jerry
Confess Don’t Confess
Jane Confess 6 60 12
Don’t Confess 12 01 1

7. Jerry
Confess
(column 3)
Don’t Confess
(column 4)
Jane Confess 6 * 60 12
Don’t Confess 12 01 1
Jane’s strategy if Jerry confesses
oThe action Jane would take if Jerry confesses.
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Best strategy for Jane: Confess (lower
jail term of 6 years)

8. Jerry
Confess
(column 3)
Don’t Confess
(column 4)
Jane Confess 6 * 60 * 12
Don’t Confess 12 01 1
Jane’s strategy if Jerry does not confess
oThe action Jane would take if Jerry does not confess.
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Best strategy for Jane: Confess (lower
jail term of 0 year)

9. Jerry
Confess
(column 3)
Don’t Confess
(column 4)
Jane Confess 6 * 60 * 12
Don’t Confess 12 01 1
What is Jane’s dominant strategy?
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Dominant strategy for Jane: Confess
(lower jail term of 6 years or 0 year)

10. Jerry
Confess Don’t Confess
Jane Confess (row 3) 6 6 *0 12
Don’t Confess (row
4)
12 01 1
Jerry’s strategy if Jane confesses
oThe action Jerry would take if Jane confesses.
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Best strategy for Jerry: Confess (lower
jail term of 6 years)

11. Jerry
Confess Don’t Confess
Jane Confess (row 3) 6 6 *0 12
Don’t Confess (row
4)
12 0 *1 1
Jerry’s strategy if Jane does not confess
oThe action Jerry would take if Jane does not confess.
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Best strategy for Jerry: Confess (lower
jail term of 0 year)

12. Jerry
Confess Don’t Confess
Jane Confess (row 3) 6 6 *0 12
Don’t Confess (row
4)
12 0 *1 1
Does Jerry have a dominant strategy?
N.B. The first number in each cell refers to jail term for Jane (blue), while
the second is for Jerry (red), if each confesses or does not confess.
Dominant strategy for Jerry: Confess
(lower jail term of 6 years or 0 year)

13. The conclusion
•Suspects are not sure of the strategies of the others; they would
confess in a bid to get a lesser jail term.
•An oligopolistic firm will adopt a dominant strategy but could do
better by cooperating or colluding.