1. Game Theory Module KRUGMAN'S MICROECONOMICS for AP* 29 65 Micro: Econ:
Margaret Ray and David Anderson

2. What you will learn in this Module:
What is game theory, and its application to oligopolies?
Can you explain the prisoner’s dilemma?
Why does frequency impact trust?
The purpose of this module is to show how game theory is used to model the decisions made by oligopolists. The module also describes a situation known as the prisoners’ dilemma and strategies through which the firms can escape the outcome predicted by the dilemma. 2

3. Game Theory
Game Theory: study of how interdependent decision makers make choices.
When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.
These strategies and mutually interdependent outcomes can be studied with game theory.
One simple definition of game theory. 3

4. Is it better to be….. Nice Clever
When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.
These strategies and mutually interdependent outcomes can be studied with game theory.
One simple definition of game theory. 4

5. In other words
...every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it. I have never known much good done by those who affected to trade for the public good.
How far can we get by trusting the invisible hand aka individual self-interest?
When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.
These strategies and mutually interdependent outcomes can be studied with game theory.
One simple definition of game theory. 5

6. In other other words Does your dorm room or classroom look like this?
When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.
These strategies and mutually interdependent outcomes can be studied with game theory.
One simple definition of game theory. 6

7. Non-Cooperative Games
Each player competes to maximize individual payoffs and ignores the effects of his/her action on the payoffs received by the rival.
When two firms are close rivals, the choices of each affect the outcomes for each. In other words, they are mutually interdependent. For example, if a retailer like Target lowers the price of a Nintendo Wii, it expects to steal customers from a store like Best Buy. And this prompts Best Buy to match the lower price on the Wii and maybe even offer something else to entice customers away from Target.
These strategies and mutually interdependent outcomes can be studied with game theory.
One simple definition of game theory. 7

8. Student’s Dilemma
Student 2
Attack
Defend
Student 1
#1: 0 Dojo
#2: 0 Dojo
#1: 5 Dojo
#2: 1 Dojo
#1: 1 Dojo
#2: 5 Dojo
#1: 3 Dojo
#2: 3 Dojo
When I call your name come to the front of the class.
Take a coin. The “1” side means attack. The “flower” side means defend.
You cannot talk! If you talk you get -1 Dojo pt. 8

9. Prisoner’s Dilemma
The payoffs are measured as years in prison, so smaller numbers are preferred.
Crook 2
Confess
Silent
Crook 1
#1: 5 years
#2: 5 years
#1: 1 year
#2: 20 years
#1: 20 years
#2: 1 year
#1: 2 years
#2: 2 years
Each player has an incentive to choose an action that benefits his/herself at the other player’s expense.
Both players are then worse off than if they had acted cooperatively.
Confession is the dominant strategy when the game is played simultaneously and they cannot talk (collude). No matter what Crook #2 does, it’s always better for Crook #1 to confess. The same is true of Crook #2’s thinking. This is the Nash equilibrium.
Characteristic of the prisoner’s dilemma is that players pursue their dominant strategy and the game comes to Nash equilibrium. However, the outcome is an undesirable one and could have been avoided through some kind of cooperative agreement (collusion). 9

10. Terms to Know
Payoff matrix: a diagram showing how the payoffs to each player in a game depend on the actions of both.
Dominant strategy: an action that allows one player to “win” regardless of what the opponent does
Nash equilibrium: occurs when the game ends, and each player is happy with the outcome, given the choice made by the rival.
Pareto optimal: occurs when the game ends, and each player gains maximum benefit. 10

11. The “sexy” dilemma
You are in a coffee shop with three of your friends. A sexy person walks in with three of their kinda cute friends.
Obviously each of you wants to hit on the sexy person.
However, if two people hit on him/her the sexy person would feel annoyed and leave.
If you hit on one kind of person and then another they will think you are gross and leave. 11

12. Business 12

13. Finding the N-Eq
What is the Nash Equilibrium in “paper-scissor- stone?”
ANSWER: Choose each one randomly about 1/3rd of the time.
What is the Nash Eq in “hei bai hei?”
ANSWER: Choose white or black randomly about ½ of the time.
DOJO: What happens if you choose exactly 1/3rd or ½ of the time? 13

14. Beyond Nash What if we can collude and play the “prisoner’s dilemma?”
Pareto Optimal: outcome where everybody is well off, and nobody can be made worse off.
What is the Pareto Optimal point in the prisoner’s game?
Under what conditions might Pareto optimality occur in real life?
The Pareto Optimal point is where both decide to stay quiet, thereby giving the best outcome for all without screwing over another.
Pareto optimality can occur [more frequently] when players are expected to play each other multiple times. Repeat behaviors can be predicted and rewarded/punished under enough iterations. This is how tacit collusion occurs in real life. 14

15. Repeated Interaction and Tacit Collusion
Repeated interaction can lead to strategic behavior
Tit for tat strategy
The “Grim Trigger”
Tacit Collusion
Strategic Behavior: taking account of the effects of an action today on the future actions of other players in the game.
One renowned strategy in game theory is one called “tit for tat”. The strategy is very simple.
The firm begins by cooperating today. Then every day from this point forward, the firm will do today, whatever the other firm did yesterday.
Tacit Collusion: cooperation among producers, without a formal agreement, to limit production and raise prices so as to raise profits. 15

16. Beyond the AP Can removing roads and bridges make traffic faster?
 Braess's paradox
Go left or right?
 The Manchester United - Chelsea Champions League Final of 2008
Should you eat your friends, but only if they don’t eat you?
 The Cannibal Puzzle
 The Market for Lemons – real world example
Strategic Behavior: taking account of the effects of an action today on the future actions of other players in the game.
One renowned strategy in game theory is one called “tit for tat”. The strategy is very simple.
The firm begins by cooperating today. Then every day from this point forward, the firm will do today, whatever the other firm did yesterday.
Tacit Collusion: cooperation among producers, without a formal agreement, to limit production and raise prices so as to raise profits. 16

17. Fuyang’s Hardest Quiz
Next week we will have a quiz. It will be the hardest quiz you will ever take at Fuyang High School.
No, seriously. I will give out AT MOST one A, and it might only be a 90%.
Anything that is not a crime is allowed. Anything. Don’t get kicked out of school for a quiz.
“If economics is a game, what are the players, teams, rules, objectives and outcomes?”
Strategic Behavior: taking account of the effects of an action today on the future actions of other players in the game.
One renowned strategy in game theory is one called “tit for tat”. The strategy is very simple.
The firm begins by cooperating today. Then every day from this point forward, the firm will do today, whatever the other firm did yesterday.
Tacit Collusion: cooperation among producers, without a formal agreement, to limit production and raise prices so as to raise profits. 17