Lecture 13(ii) Announcements

None

Lecture on Game Theory

1. The Simple Version of the Battle of the Sexes

2. The Battle of the Sexes with Some Strategic Moves

3. Rock Paper ‘Scissors

4. Chicken

5. Duopoly

Stay Silent

Confess

Stay Silent

F gets 8Friday

Confess

R gets 8 R gets 20

R gets 1R gets 0

F gets 20 F gets 1

F gets 0

Recall Prisoner’s Dillemma

Nash Equlilibrium:

Both Confess

In this game confessing is a

dominant strategy

Robinson

Watch SYTTD

Watch Football

Watch SYTTD

M gets 3Male

Watch Football

F gets 1 F gets 0

F gets 3F gets 0

M gets 0 M gets 1

M gets 0

The Battle of the Sexes

Suppose the two players simultaneously make their choice. Let’s figure out the optimal strategy for each player

Female

Look at incentives for the male player:

Suppose he thinks girl is going to watch football....

Suppose he thinks the girl is going to watch SYTTD.

Look at incentives for the female player:Suppose she thinks guy is going to watch football....

Suppose she thinks the guy is going to watch SYTTD...

What are the Nash Equilibria of this simultaneous-move game?

Let’s change the game so that the action is sequential.

Girl moves first. Sends text message to guy about her decision. Then guy moves. What is the equilibrium outcome now if the guy rationally optimizes given the girl’s choice?

First Mover Advantage

Lets change it one more time. Like above, girl picks show before guy, and sends text message to guy, after picking her show..

But before the girl picks her show, the guy makes a deal with all his friends that if any of them hears that he watched SYTTD, they all will defriend him on Facebook. Suppose the guy really likes having Facebook friends, and if he is defriended by all the guys he suffers a loss of 10.

After this move, the payoffs look like:

Watch SYTTD

Watch Football

Watch SYTTD

M gets 3Male

Watch Football

F gets 1 F gets 0

F gets 3F gets 0

M gets 0 −10 = −10

M gets 1 − 10 = − 9

M gets 0

The Battle of the SexesIf guy is defriended fromwhen he watches SYTTD.

Now work out the equilibrium when each player is forward-looking and assumes the other player will play

Female

rationally, given the choices already made by the other player. To solve this, need to work backwards and look at the endgame.

Suppose guy strikes the deal with his friends to defriend him if he watches SYTTD.

Then regardless girl’s choice, in the endgame, guy will choose __________

Anticipating guy’s behavior, girl will choose _________

Anticipating how girl will respond to pact with friends, guy will make the pact.

This move on the guy’s part is something like the famous example of Cortez burning his ships after landing in Mexico in 1519. He was playing a game with his soldiers. Fighting the Aztec Indians then became a better option for the soldiers than retreating back to the ships.

This is a taste of game theory. More than being fun and interesting, it is a powerful tool for social scientists to study important strategic interactions. (Mention this because this is a Social Science Core Class)

Test your knowledge: What is Nash equilibrium when Robinson and Friday play rock, paper, scissors game?

How about:Robinson picks rockFriday picks scissors

Now game of Chicken

Suppose red person can convince blue person that he is totally OK with both players playing "straight" and smashing into each other. Then blue will play "swerve," seeing that red will play "straight." In a game of chicken, reputation for being crazy helps you win.

Application to 2013 debt ceiling negotiationsPerhaps can think of republicans were red player above, claimed fine to breach debt ceiling. Obama called their bluff.

Maybe more a hostage situation.

2015 debt ceiling negotiationsObama took credible position not to give anything

Tea party took credible position to run out of town a house speaker to could raise the debt ceiling

Equilibrium of this endgame: The then speaker (John Boehner)and to say he was going to resign, and then get debt ceiling raised before new speaker Paul Ryan took the job.

Duopoly In EconlandGoldy and Bucky have entered Widgit

business

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10

0 1 2 3 4 5 6 7 8 9 10

D

MC=ATC

MR

With perfect comp, get Q =___ P=___With monopoly, get Q = ___, P = ___What happens with duopoly?It depends. Let’s look at some cases.

1. Have to post prices, stay that way for the entire day.

2. Have to be a round number.

3. Buyers buy from the lowest price firm. If prices the same, then the sellers split the market.

4. For now, look at prices 6 and 5.

Let’s suppose we have the scenario above. Let’s work out what happens.

We will need to map this into the prisoner’s dilemma payoff matrix from the previous lecture.

Payoff MatrixHow Profit Depends Upon

Both Actions

Goldy

B gets

B gets B gets

G gets G gets

G gets G gets

P = 6

Bucky B gets

P = 5

P = 6

P = 5

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10

0 1 2 3 4 5 6 7 8 9 10

D

MC=ATC

MR

Suppose both set P = 6. Then total quantity is Q = 4, and the split it 50/50, so q = 2 for each.

Profit for each is____So put this in Payoff Matrix when both set P = 6.

Suppose both set P = 5.Then total quantity is Q = 5, and they split the market 50/50, so q = 2.5 for each.

Profit for each is ______So put this in the Payoff Matrix for the profit each gets when both set P = 5.

If one sets P=5 and the other P=6.

Looking at this payoff matrix, we see:

Dominant Strategy?

If could cooperate?

Other prices?1. P = 7 is monopoly price. But....

2. P = 4?

So Nash Equilibrium is....