Review

From last time:

I Strategy A strictly dominates strategy B if the payoff from Ais higher than the payoff of B, regardless of others’ strategies

I Moral: you should never pick a dominated strategy

I Moral: If you don’t have a dominated strategy, try to predictyour opponents’ choice

Review

From last time:

I Strategy A strictly dominates strategy B if the payoff from Ais higher than the payoff of B, regardless of others’ strategies

I Moral: you should never pick a dominated strategy

I Moral: If you don’t have a dominated strategy, try to predictyour opponents’ choice

Review

From last time:

I Strategy A strictly dominates strategy B if the payoff from Ais higher than the payoff of B, regardless of others’ strategies

I Moral: you should never pick a dominated strategy

I Moral: If you don’t have a dominated strategy, try to predictyour opponents’ choice

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if

ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Notation

I Let 1, 2, . . . , n denote players

I Let si denote a particular strategy of player i

I Let Si denote the set of all strategies of player i

I Let s−i denote a choice of strategy for all players exceptplayer i

I Let ui (si , s−i ) denote the utility/payoff for player i if playerschoose strategies si/s−i

I So si strictly dominates s∗i if ui (si , s−i ) > ui (s∗i , s−i ) for all

choices of s−i

Sacking Rome

I Hannibal wants to cross into Italy with two batallions

I There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coast

I Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallion

I Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions brought into countryand # of batallions die

Sacking Rome

I Hannibal wants to cross into Italy with two batallions

I There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coast

I Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallion

I Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking Rome

I Hannibal wants to cross into Italy with two batallionsI There are two options:

I Easy path along the coastI Hard path through the Alps

I If he takes the hard path, he loses one batallion (just fromcrossing)

I If he meets the defending army, he loses one batallionI Is this a game?

I Need payoffs - let’s use # of batallions that die/are broughtinto Italy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?

I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategies

I Hannibal has a weakly dominant strategyHe’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−i

I What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

Sacking RomeThe outcome matrix is:

E HE

H

1, 1

2,0 0,2

1,1Fabius

Hannibal

I You are Fabius Maximus. What should you do?I Are there any dominant strategies?

I No strictly dominat strategiesI Hannibal has a weakly dominant strategy

He’ll probably choose to take the easy route

I si weakly dominates s∗i if ui (si , s−i ) ≥ ui (s∗i , s−i ) for all

choices of s−iI What does this mean?

I Strategy si weakly dominates strategy s∗i if the payoff from siis never worse than the payoff of s∗i , regardless of others’strategies

I Moral: you should probably never pick a weakly dominatedstrategy

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)

I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in class

I They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

Review:

I Everyone in class wrote down their name and a numberbetween 1 and 100

I I took 23 the average of everyones’ numbers

I Whoever is closest wins $5 − (.01) · (how far they are off)I Example:

I Suppose that there are three people in classI They choose 5, 30, 55

I2

3· 5 + 30 + 55

3= 20

I 30 wins $4.90

The Numbers Game

I Why might someone choose ≈ 33?

I If everyone else chooses randomly, the average will be ≈ 50I Two thirds of the average will be ≈ 33

I Any problems?

I If most people think this way, the average will be ≈ 33, and sotwo thirds of the average will be ≈ 22

The Numbers Game

I Why might someone choose ≈ 33?I If everyone else chooses randomly, the average will be ≈ 50

I Two thirds of the average will be ≈ 33

I Any problems?

I If most people think this way, the average will be ≈ 33, and sotwo thirds of the average will be ≈ 22

The Numbers Game

I Why might someone choose ≈ 33?I If everyone else chooses randomly, the average will be ≈ 50I Two thirds of the average will be ≈ 33

I Any problems?

I If most people think this way, the average will be ≈ 33, and sotwo thirds of the average will be ≈ 22

The Numbers Game

I Why might someone choose ≈ 33?I If everyone else chooses randomly, the average will be ≈ 50I Two thirds of the average will be ≈ 33

I Any problems?I If most people think this way, the average will be ≈ 33, and so

two thirds of the average will be ≈ 22

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rational

I Every player assumes every other player is completely rational

I Are any strategies weakly dominated?

I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?

I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?

I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?I 68 through 100

I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

Iterative Deletion of Dominated Strategies

I Assume:I Every player is completely rationalI Every player assumes every other player is completely rational

I Are any strategies weakly dominated?I 68 through 100I Cross these strategies out for everybody

I After crossing these strategies, are any strategies weaklydominated?

I 46 through 67

I If we continue this process, everyone is left with choosing 1

The Numbers Game

I The class’ numbers were:1, 1, 1, 2.14, 15, 15, 17.9, 18, 30, 32, 34, 34, 37, 45, 45, 48, 48, 53, 80, 89

I Two thirds of the average is 21.53

I Congratulations Andre Serrano ($4.80)

The Numbers Game

I The class’ numbers were:1, 1, 1, 2.14, 15, 15, 17.9, 18, 30, 32, 34, 34, 37, 45, 45, 48, 48, 53, 80, 89

I Two thirds of the average is 21.53

I Congratulations Andre Serrano ($4.80)

The Numbers Game

I The class’ numbers were:1, 1, 1, 2.14, 15, 15, 17.9, 18, 30, 32, 34, 34, 37, 45, 45, 48, 48, 53, 80, 89

I Two thirds of the average is 21.53

I Congratulations Andre Serrano ($4.80)

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?

I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”

2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”

3. “Everyone knows that everyone knows that everyone knowsthe strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

The Numbers Game

I Let’s play this game again

I Write down a number between 1 and 100

I Who wrote a lower number than last time?I What changed?

I Strategies for the game became common knowledge:

1. “Everyone knows the strategy”2. “Everyone knows that everyone knows the strategy”3. “Everyone knows that everyone knows that everyone knows

the strategy”

4....

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

Assume:

I There is a spectrum of 10 points on a certain political issue

I There are two candidates

I 10% of the voters hold each position

I Voters will vote for the candidate who holds the closest views

I If the candidates hold the same view, they’ll split the vote

Is this a game?

I Have players (the candidates)

I Have strategies (1 − 10)

I Need payoffs: choose the % of the vote that they earn

Political Spectrum

I Are there any dominated strategies?

I 1 is weakly dominated by 2I 10 is weakly dominated by 9

I Anything else?

I 3 does not dominate 2but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”

Political Spectrum

I Are there any dominated strategies?I 1 is weakly dominated by 2

I 10 is weakly dominated by 9

I Anything else?

I 3 does not dominate 2but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”

Political Spectrum

I Are there any dominated strategies?I 1 is weakly dominated by 2I 10 is weakly dominated by 9

I Anything else?

I 3 does not dominate 2but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”

Political Spectrum

I Are there any dominated strategies?I 1 is weakly dominated by 2I 10 is weakly dominated by 9

I Anything else?I 3 does not dominate 2

but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”

Political Spectrum

I Are there any dominated strategies?I 1 is weakly dominated by 2I 10 is weakly dominated by 9

I Anything else?I 3 does not dominate 2

but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”

Political Spectrum

I Are there any dominated strategies?I 1 is weakly dominated by 2I 10 is weakly dominated by 9

I Anything else?I 3 does not dominate 2

but after we remove 1 it does (assuming common knowledge)

I If we iterate this, the candidates end up in the centralpositions

I This is The Median Voter Theorem“Majority rule voting will select the median preference”