ECON 101 Tutorial: Week 8

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ECON 101 Tutorial Week 8

• Shane Murphy
• s.murphy5_at_lancaster.ac.uk
• Office Hours Monday 300-400 LUMS C85

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LUMS Maths and Stats Help (MASH) Centre

• Are you mystified by maths? Stuck with
  statistics? The LUMS Maths and Stats Help (MASH)
  Centre for LUMS undergraduate students opens this
  week. Every Monday (16.00-18.00) and Friday
  (10.00-12.00), you can drop-in to LUMS B38a or
  book an appointment to see a student mentor and
  get help with maths and stats

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Outline

• Roll Call
• Bonus
• Problems
• Discussion

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Bonus

• Box of Lies
• Melissa McCarthy
• Emma Stone
• Kate Hudson
• Channing Tatum
• Tina Fey
• Jennifer Lawrence
• Julie Bowen
• Kerry Washington
• Kate Hudson
• You pick

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Exercise 1

• If a player has a dominant strategy in a
  simultaneous-move game, then she is sure to get
  her best possible outcome. True or false?
  Explain and give an example of a game that
  illustrates your answer.
• False. The Prisoners Dilemma is a counter
  example.

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Exercise 2

• Consider the following simultaneous game
• Find the Nash equilibrium or equilibria.
• A up B left
• Which player, if any, has a dominant strategy?
• A up B none
• Write down the extensive form for this game,
  played with simultaneous moves.
• Suppose the game is now sequential move, with A
  moving first and then B. Write down the extensive
  form for this sequential move game.
• Write down the normal form for the sequential
  move game. Find all the Nash equilibria.

Player A\B Left Right
Up 3, 3 5, 1
Down 2, 2 4, 4
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Exercise 2

• Consider the following simultaneous game
• Write down the normal form for the sequential
  move game. Find all the Nash equilibria.
• There are 2 Nash Equilibria
• A Up and B Left Up, Left Dawn
• A Down and B Left Up, Right Down
• This is also a subgame perfect equilibrium

Player A\B LeftUp LeftDown LeftUp RightDown RightUp LeftDown RightUp RightDown
Up 3, 3 3,3 5, 1 5,1
Down 2, 2 4,4 4, 4 4,4
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Exercise 3

• Two classmates A and B are assigned a group
  project. Each student can choose to Shirk or
  Work. If one or more players choose Work, the
  project is completed and gives each student some
  credit valued at 4 payoff units each. The cost of
  completing the project is that 6 total units of
  effort (measured in payoff units) are divided
  equally among all the players who choose to Work
  and this is subtracted from their payoffs. If
  both Shirk, they do not have to expend any effort
  but the project is not completed, giving each a
  payoff of 0. The teacher can only tell whether
  the project is completed and not which students
  contributed to it
• Find the NE
• Both Shirk
• Find the Dominant Strategy, what game is this
  similar to?
• Shirk for both This is equivalent to the PD

Player A\B Shirk Work
Shirk 0,0 4,2
Work -2,4 1,1
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Exercise 3

• Two classmates A and B are assigned a group
  project. Each student can choose to Shirk or
  Work. If one or more players choose Work, the
  project is completed and gives each student some
  credit valued at 4 payoff units each. The cost of
  completing the project is that 6 total units of
  effort (measured in payoff units) are divided
  equally among all the players who choose to Work
  and this is subtracted from their payoffs. If
  both Shirk, they do not have to expend any effort
  but the project is not completed, giving each a
  payoff of 0. The teacher can only tell whether
  the project is completed and not which students
  contributed to it
• Find the NE
• Both Shirk
• Find the Dominant Strategy, what game is this
  similar to?
• Shirk for both This is equivalent to the PD

Player A\B Shirk Work
Shirk 0,0 4,2
Work -2,4 1,1
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Exercise 4

• Verify the following game is a version of the
  Prisoners Dilemma

Player A\B Confess Silent
Confess 0, 0 3, -1
Silent -1, 3 1, 1
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Exercise 5

• Im not comfortable teaching this, luckily we are
  low on time and can skip it.

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Exercise 6

• Identify Nash equilibria in pure strategies (if
  any) and explain your findings. In particular,
  consider whether players know which (if any) Nash
  equilibrium will result.
• Two NE Firm 1 Enters, Firm 2 does not
• Firm 2 Enters, Firm 1 does not
• Without collusion, we dont really expect either
  to occur.

Firm 2\Firm 1 Do not enter Enter
Do not enter 0, 0 0, 1
Enter 1, 0 -1, -1
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Exercise 7

• Belgium has few traffic signs or signals and does
  not have a give-way rule. A driver in Belgium who
  stops to look both ways at an intersection loses
  the legal right to go first. Using the Game of
  Chicken, explain why Belgium has more per capita
  accidents at unmarked intersections resulting in
  bodily injury compared to neighbouring countries
  which have more stop signs and traffic lights and
  explicit rules about right of way.
• What?!? In America we have stoplights. This
  question is crazy
• When a man and a woman approach a door at the
  same time, it is customary for the man to let the
  woman go first. Use the Game of Chicken to
  explain this social convention.
• What?!? I dont see gender. I only see souls.

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Exercise 8
BA\Air France QA 96 64 48
QB 96 0, 0 3.1, 2 4.6, 2.3
64 2, 3.1 4.1, 4.1 5.1, 3.8
48 2.3, 4.6 3.8, 5.1 4.6, 4.6

• Above is the normal-form representation of a game
  between British Airways and Air France where each
  chooses between three possible actions fly 96,
  64 or 48 thousand passengers between Manchester
  and Paris, with payoffs as m profits per
  quarter.
• Is there a strictly dominant strategy for this
  game?
• No.
• Use iterated elimination of strictly dominated
  strategies to find an outcome for the game
• AFs QA96 is strictly dominated by QA 64
• BAs QB 96 is strictly dominated by QB 64
• From what remains, 48 is dominated by 64 for
  each firm.
• So the equilibrium is QA QB 64
• List the assumptions you made to discover the
  game outcome.
• The iterated approach relies on
• the belief that players wont choose strictly
  dominated strategies.
• Players possess common knowledge that they are
  payoff maximising
• Players know that other players are payoff
  maximizing
• etc

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Exercise 9

• The entrant moves first and the incumbent
  observes the entrants decision. The entrant can
  choose to either enter the market or remain out
  of the market. If the entrant remains out of the
  market then the game ends and the entrant
  receives a payoff of 0 while the incumbent
  receives a payoff of 2. If the entrant chooses to
  enter the market then the incumbent gets to make
  a choice. The incumbent chooses between fighting
  entry or accommodating entry. If the incumbent
  fights the entrant receives a payoff of -3 while
  the incumbent receives a payoff of -1. If the
  incumbent accommodates the entrant receives a
  payoff of 2 while the incumbent receives a payoff
  of 1. Solve this game.

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Exercise 9

• The entrant moves first and the incumbent
  observes the entrants decision. The entrant can
  choose to either enter the market or remain out
  of the market. If the entrant remains out of the
  market then the game ends and the entrant
  receives a payoff of 0 while the incumbent
  receives a payoff of 2. If the entrant chooses to
  enter the market then the incumbent gets to make
  a choice. The incumbent chooses between fighting
  entry or accommodating entry. If the incumbent
  fights the entrant receives a payoff of -3 while
  the incumbent receives a payoff of -1. If the
  incumbent accommodates the entrant receives a
  payoff of 2 while the incumbent receives a payoff
  of 1. Solve this game.

Entrant
Enter
Dont Enter
Incumbent
I 2, E 0
Fight
Accomodate
I -1, E -3
I 1, E 2
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Exercise 9

• The entrant moves first and the incumbent
  observes the entrants decision. The entrant can
  choose to either enter the market or remain out
  of the market. If the entrant remains out of the
  market then the game ends and the entrant
  receives a payoff of 0 while the incumbent
  receives a payoff of 2. If the entrant chooses to
  enter the market then the incumbent gets to make
  a choice. The incumbent chooses between fighting
  entry or accommodating entry. If the incumbent
  fights the entrant receives a payoff of -3 while
  the incumbent receives a payoff of -1. If the
  incumbent accommodates the entrant receives a
  payoff of 2 while the incumbent receives a payoff
  of 1. Solve this game.

Entrant
Enter
Dont Enter
Incumbent
I 2, E 0
Fight
Accomodate
I -1, E -3
I 1, E 2
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Exercise 9

• The entrant moves first and the incumbent
  observes the entrants decision. The entrant can
  choose to either enter the market or remain out
  of the market. If the entrant remains out of the
  market then the game ends and the entrant
  receives a payoff of 0 while the incumbent
  receives a payoff of 2. If the entrant chooses to
  enter the market then the incumbent gets to make
  a choice. The incumbent chooses between fighting
  entry or accommodating entry. If the incumbent
  fights the entrant receives a payoff of -3 while
  the incumbent receives a payoff of -1. If the
  incumbent accommodates the entrant receives a
  payoff of 2 while the incumbent receives a payoff
  of 1. Solve this game.

Entrant
Enter
Dont Enter
Incumbent
I 2, E 0
Fight
Accomodate
I -1, E -3
I 1, E 2
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Discussion

• Box of Lies
• Melissa McCarthy
• Emma Stone
• Kate Hudson
• Channing Tatum
• Tina Fey
• Jennifer Lawrence
• Julie Bowen
• Kerry Washington
• Kate Hudson
• You pick again!