Game Theory
Game theory is a “science” that helps us better understand why and how people make certain
decisions. As a class we will simply scratch the surface of this interesting subject but I encourage all
students to dig deeper into understanding the mathematics of each game.
In short, game theory will consist of a story that puts you and your classmates in a position to make a
decision. Your goal is to maximize your “payoff” also know in economic terms as a utility. In its
simplest terms a utility measures how much your situation is improved or how much satisfaction you
would draw from your decision. In Game theory, payoffs may be explained in specific detail or with
assigning a number.
There are literally 1000’s of games that have been developed in game theory. We will “play” games
that have strong connections to our course.
As we play these games it is important that you make connections to real-life situations and also
recognize the limitations of each game, in other words what is and isn’t the game teaching us?
It is my belief that Game Theory even in its simplest form will help the students bring both
Government and Economics together.
When playing games students should always think about the following items:
1.
2.
3.
4.
5.
6.
7.
Play dominate strategies that best maximize your payoffs
Make rational choice based on your information
Know your self interest
Put yourself in other’s shoes
Eliminate weaker options so that you are left with the Best Response
Think Strategically- anticipate (look forward and reason backward)
Cooperation must be enforced
Games for Unit 1
Prisoner’s Dilemma- What happens when self interests compete and each self interest is the dominant
or best response to a situation?
Rock Paper Scissors- Understanding the Free Market, Command Economies, decision making, and the
government’s role. Mixed strategies and zero sum games.
Stag (Deer) Hunt- Cooperation or self-interest? When is your best response to cooperate?
The Chip Game- A combination of competition, cooperation, and trust.
Prisoner’s Dilemma
Story: Two men are arrested for a crime. The police have enough evidence to convict both for a lesser
crime. By itself this crime would give each prisoner 6 months. The police are certain that both prisoners
worked together to commit a more serious crime. If convicted each prisoner would receive 10 years for
the more serious crime. The only way that the police will be able to convict each criminal is if they
either confess or rat the other out. The police put each prisoner in a separate cell and present the deal
diagramed below to each the prisoner. What should each prisoner do? Why?
Prisoner 2
(Confess) Rat out other prisoner
(Confess)Rat out other prisoner
Stay Silent
3 years, 3 years
0 years, 10 years
10 years, 0 years
6 months, 6 months
Prisoner 1
Stay Silent
Questions:
1.
2.
Is there a dominate strategy? In terms of years what is the best decision to make- always?
Putting yourself in the other’s shoes what do you think the other prisoner will do? What should
you do?
3. Besides time served in jail what are some other possible utilities that may be considered by each
prisoner?
4. If both decided in advance to remain silent, how sure could they be that the other prisoner
would keep hi word? What could be some ways to “force” cooperation?
5. Think of or research some real “prisoner’s dilemmas in our government or economy.
In class Prisoner’s dilemma
Student 2
Alpha
Beta
Alpha
B-, B-
A, C+
Beta
C+, A
B+, B+
Student 1
1. Consider the questions above for Prisoner’s Dilemma.
2. Would you change your strategy if you knew that you would be playing this game multiple times
as opposed to just once? Why?
3. Relate question 2 to the government and the economy?
Rock-Paper-Scissors (mixed strategies)
Player 2
Player 1
Rock
Paper
Scissors
Rock
0, 0
0, 1
1, 0
Paper
1, 0
0, 0
0, 1
Scissors
0, 1
1, 0
0, 0
1. In the absence of a clearly dominating strategy what is the best strategy?
2. What are some methods to better your chances of winning?
Capitalism game:
1.
2.
3.
4.
In your own words define the word- Fair.
How much of advantage or disadvantage is the starting position?
Was this game fair?
Would you do something different if you played this game again? Would you become better?
Why and why not?
5. What are some ideas or rules that could be put in place to help the “poor?” Would this be fair?
Would these rules encourage players to improve? Explain why or why not.
6. This game is a zero-sum game, meaning the end result is zero. Someone wins and someone
loses. Is capitalism a zero-sum game?
Communism game:
1. Was this game more or less fair than the previous game? Explain why or why not?
2. Was this game more or less productive? In this game productivity being measured as the
amount of games played?
3. Compare or contrast the role of government (teacher) in this game with the role of the teacher
in the last game. Did the teacher make the game better or worse? Explain why it was better or
worse.
4. Did this game encourage creativity? Why or why not?
Stag Hunt (Deer Hunt)
According to Jean-Jacques Rousseau, in his view of the Social Contract
“The passage from the state of nature to the civil state produces a very remarkable change in man, by
substituting justice for instinct in his conduct, and giving his actions the morality they had formerly
lacked. Then only, when the voice of duty takes the place of physical impulses and right of appetite,
does man, who so far had considered only himself, find that he is forced to act on different principles,
and to consult his reason before listening to his inclinations. Although, in this state, he deprives himself
of some advantages which he got from nature, he gains in return others so great, his faculties are so
stimulated and developed, his ideas so extended, his feelings so ennobled, and his whole soul so
uplifted, that, did not the abuses of this new condition often degrade him below that which he left, he
would be bound to bless continually the happy moment which took him from it for ever, and, instead of
a stupid and unimaginative animal, made him an intelligent being and a man.”
To illustrate this idea Rousseau developed a game called Stag Hunt.
Story: Villagers go on a hunt. If they cooperate and hunt the stag (deer) the potential reward if greater
than if they hunt on their own and only capture a rabbit. They need to be patient and work together for
the stag or they can go out on their own and kill the rabbit which would be easier but would also
jeopardize the chances for the other hunters.
Hunter 2
Stag
Rabbit
Stag
2, 2
0, 1
Rabbit
1, 0
1, 1
Hunter 1
1. Should a hunter’s priority be himself and his family or the village? Explain?
2. What does this story tell us about social cooperation?
3. Does the village have the right to tell a specific hunter that they cannot hunt for rabbit if they
feel that it will prevent the village from eating a Stag? Why or why not explain your reasoning.
4. Relate to Individual rights and purposes of government.
5. Relate to economic liberty and economic equality.
6. Make the connection between external cost and the stag hunt.
The Chip Game
5- Red- 100, 10- Blue- 50, 20- Yellow- 20, 25- White- 10
1. How did the group/individual win the game?
2. For individuals who decided to create alliances- in order to ensure that you were not taken
advantage of what kind of arrangements did you make?
3. Would simply trusting another person make sense? Why or why not?
4. Why would not creating an alliance also put you in a dominated position?
5.
“The accumulation of all powers, legislative, executive, and judiciary, in the same hands,
whether of one, a few, or many, and whether hereditary, self-appointed, or elective, may justly be
pronounced the very definition of tyranny”
According to this game is James Madison correct?