MGEB13-15

8/12/2019 MGEB13-15

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Managerial Economics

Session 15

Introduction to Game Theory

Simultaneous move games and Nash equilibrium

Price competition in duopoly – Battlefield Iberia

Sequential moves – First mover’s advantage

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Welcome to the world of pirates: EQ = 0 IQ > 140

A tale of pure conflict

Black-hole Brandon is the captain of the pirate ship Macarenawith four other pirates under his command. Second incommand is Black Jack. Jack Sparrow and Jack Daniels arethird and fourth in command respectively, and Junior Brandonis the junior most.

Rules of the ship

• The captain always proposes a distribution of the loot. All pirates vote on the proposal, and if half the crew or more go

"Aye", the loot is divided as proposed.• If the captain fails to obtain support of at least half his crew

(including him), he have to walk the plank.

• When the captain gets displaced (murdered, to be precise),

the next in command becomes the captain.

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Dividing the loot – a test of intelligence

• The pirates looted a ship and obtained 100 chests of gold.

• The captain will have to divide the loot among 5 of them.

• The smallest denominator should be chest.

• The pirates are all

– extremely intelligent (IQ > 140) and emotionless (EQ = 0),

unlike most human beings

– treacherous (SQ = 0), like most human beings, and

– selfish (HQ = 0), like ALL human beings.

• What is the maximum number of chests the captain cankeep without risking his life?

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Are you really “rational”?

• Suppose I give you ten Rs. 10 notes, which are to bedivided between you and your friend.

• You propose a division (without consulting your friend)

• If s/he accepts, fine.

• On rejection, I take back six notes. Now your friend gets tocounter propose a division of the remaining four notes.

• If you accept, fine.

• If you reject, I take back the remaining four notes and the

game is over.• Let’s play.

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Homo Economicus

• "Every individual... neither intends to promote the

public interest, nor knows how much he is

promoting it. By pursuing his own interest hefrequently promotes that of the society more

effectually than when he really intends to promote

it.”

– Adam Smith (The Wealth of Nations)

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Fundamental Objectivism

• "I swear by my life, and my love of it, that I

will never live for the sake of another man,nor ask another man to live for mine.”

– Ayn Rand (Atlas Shrugged)

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The Essential “Game” Environment

Players

• Everyone who has an effect on your earnings

Strategies

• Actions available to each player

• Define a plan of action for every contingency

Payoffs

• Numbers associated with each outcome• Reflect the interests of the players

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Characterizing Games

What characterizes a game?

Timing of moves

• Are moves simultaneous or sequential?

Nature of conflict and interaction

• Are players’ interests in conflict?

• Will players interact once or repeatedly?

Informational conditions• Are some players better informed?

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A Russian Fairytale

In May 1878, a musician named Vladimir Tschesnokoff boarded a

train from Belorussky terminal, Moscow. He was traveling toInnsbruck to play violin backstage of Tchaikovsky’s Swan Lake.

Tschesnokoff was detained for possessing music notations, which

were thought to be spy codes. The Russo-Turkish war just ended

and Russia’s relation with Austria-Hungary was strained.

Tschesnokoff was told that Tchaikovsky was also detained andwas being interrogated at Saint Petersburg.

Tschesnokoff knew Tchaikovsky, as Tchaikovsky was by then

famous in the music community. But Tchaikovsky didn’t know

Tschesnokoff, and Tschesnokoff was aware of the fact.

Baseline Situation:• Two suspects, who don’t know each other, are being interrogated.

• There is no proof of the alleged crime.

• A confession from the prisoner(s) is required.

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The deal

The prisoners were given the following deal: – They could either “confess” or “not confess”

– If both did “not confess”, each would remain in prison for

1 year.

– If both did “confess”, each would remain in prison for 5years.

– If one did “not confess” and the other “confessed” then

the one who “confessed” would have been set free if he

testified against the other who did “not confess”. The onewho did “not confess” would remain in prison for 10

years.

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Prisoner’s Dilemma

• C – confess, N – not confess

C N

C -5, -5 0, -10

N -10, 0 -1, -1

Prisoner 1

Prisoner 2

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Learning from Prisoner’s Dilemma

Selfishness (pursuing ones own interest) does not

necessarily maximize social welfare

Adam Smith wasn’t exactly right.

An equilibrium is NOT necessarily efficient

Players can be forced to accept

mutually bad outcomes

Bad to be playing a prisoner’s dilemma,

but good to make others play

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Battleground Iberia – Boeing vs. Airbus

In 2002-3, Iberia wanted to buy 12 planes.

Options: Boeing’s 777 and Airbus’ A340

Enrique Dupuy, Iberia’s CFO, invited Boeing’s top

sales executive Toby Bright and offered to get its 6 old

747s replaced by 12 new 777s in its long-haul South

American sector.

Asked for discount. He threatened Boeing that Iberia

might go for an all-Airbus fleet.

Since 1995, Iberia never did business with Boeing.

Dupuy contacted Airbus’ John Leahy too

Asked for 40% discount. He said he’ll get Boeing offer

50%. For Airbus, Iberia was crucial turf to defend.

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Iberia passed on the message that they “really” wanted

two suppliers.

“With over 200 airlines and only 2 plane makers, we thinkwe deserve a little more respect.” – John Leahy

Boeing didn’t want to compete. But Dupuy needed

Boeing! (How else can he make the titans play the

Prisoner’s Dilemma?) Toby Bright knew that!

“You are going out of your ways to show us. Are we being

brought in as a stalking horse?” – Toby Bright

Eventually Iberia bought 9 A340s at an undisclosed price. The exact price is was not disclosed.

“Everything had been structured to maintain tension up to

the last 15 minutes.” - Dupuy

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Grab the deal!

Firm 2

High disc. Low disc.

Firm 1High 300, 300 600 , 0

Low 0 , 600 450 , 450

Equilibrium: $300Mn

Cooperation: $450 Mn

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Another Prisoner’s Dilemma:

Cigarette Advertising on TV

• Players: Reynolds and Philip Morris

• Strategies: Advertise or Not Advertise

• Payoffs: Companies’ Profits

• Payoff landscape:

– Each firm earns $60 million from its customers

– Advertising costs a firm $30 million – Advertising captures $40 million from competitor, ifthe competitor is not putting ads.

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The Advertising Dilemma

PLAYERS

STRATEGIESPAYOFFS

Philip Morris

No Ad Ad

Reynolds

No Ad 60 , 60 20 , 70

Ad 70 , 20 30 , 30

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Dilemma resolved

• All US tobacco companies advertised heavily on TV

• Surgeon General issues official warning• Cigarette smoking may be hazardous

• Cigarette companies fear lawsuits

• Government may recover healthcare costs

• Companies strike agreement• Carry the warning label and cease TV advertising

in exchange for immunity from federal lawsuits.

• Cigarette advertising decreased by $63 million• Industry profits increased by $93 million

1964

1970

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Modified game –

Incorporating an expected cost of lawsuit

Philip Morris

No Ad Ad

Reynolds

No Ad 60 , 60 20 , 50

Ad 50 , 20 10 , 10

$ 20 million is the expected cost of lawsuit.

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Dominant strategy

• Strictly dominant strategy: A strategy of player, is

strictly dominant if for any strategy of the rival,

s/he is strictly better-off playing this strategy vis-à-

vis any other available strategy.

• Weakly dominant strategy: A strategy of player, is

weakly dominant if for any strategy of the rival,

s/he is better-off or as well off playing this strategy

vis-à-vis any other available strategy.

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Nash Equilibrium

The outcome of a game when rational players interact

• Each player is playing his or her best strategy given

the strategy choices of all other players. A strategy profile constitutes a Nash equilibrium if the

strategies are best responses to each other.

• No player has incentive to change his or her action

unilaterally

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Commandment 1

• If you have a dominant strategy, use it

• Expect your opponent to use her if she has

got one.

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If there isn’t any Dominant Strategy?

Often there is no dominant strategy

Some games may have multiple equilibria

Equilibrium selection becomes an issue

Method:

For each player, find the best response to every strategy of

the other player

Games of Coordination

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Developing the super-jumbo:

Airbus vs. Boeing again!

• Airbus lacked a jumbo jet:

– “ The problem is the monopoly of the 747…They have

a product. We have none. ” - Airbus press release, 1993

– Initiated plans to build a super-jumbo jet

• Industry feasibility studies:

– Need for super-jumbos for long-hauls. Room for atmost one.

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The strategic game

• D – develop, N – not develop

D N

D -7, -7 5, 0

N 0, 5 0, 0Airbus

Boeing

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Sequential Game – First mover’s advantage

• Boeing preemption strategy:

– “Boeing, the world’s top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and mostexpensive airliner ever.” -BusinessWeek, 1993

Boeing

Airbus

Airbus

5, 0

D

N

N

D

N

D

-7, -7

0, 0

0, 5

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• We all know what a difference 14 years made!• A380 made its first commercial flight from Singapore toSydney on 25th October, 2007.

• As of August 2012 there had been 257 confirmed orders forthe A380, of which 81 have been delivered.

• Airbus announced the plan to develop A380 back in June1994

• What the analysts had to say in January 1993?

• “On January 5, Boeing, the world’s top aircraft maker,

announced it was building a plane with 600 to 800 seats, thebiggest and most expensive airliner ever. Some in the industry

suggest Boeing’s move is a bluff to preempt Airbus from

forging ahead with a similar plane.”

~ BusinessWeek, 1993

Was Boeing’s preemption strategy credible?

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“Доверяй, Но Проверяй”(“doveryai, no proveryai”) “Trust, but verify”

- Russian Proverb

You cannot get the first mover’s advantage unless you arecredible.

• What could have made Boeing’s threat credible?

• R&D joint venture with one of the engine manufacturers• GE and Rolls Royce are the only two engine manufacturers.

Why didn’t they do so? They did not have any plan to develop the aircraft and it

was a preemption strategy to save the market for 747

Credibility is the issue

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First mover’s advantage to Airbus

Airbus forged ahead and made first physical investments indevelopment of A-380.

Airbus

Boeing

Boeing

5, 0

D

N

N

D

N

D

-7, -7

0, 0

0, 5

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If a game is sequential…

• Look forward and reason back.

• Anticipate what your rivals will do in response to youraction

• Thinking backwards is easy in game trees

– Start at the end and trim the tree to the present

• Thinking backwards is challenging in practice

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Commandment 2

Look forward, reason backward…putyourself in your rival’s shoes…try to see

through your rival’s strategy

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MGEB13-15

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