CS计算机代考程序代写 android Hive Oligopoly

Oligopoly
Competition in markets

Structure

LT4.t1 : Applying GT

LT4.t2 : Commitment

LT4.t3 : Cooperation?

LT4.t4 : Axelrod

LT4.t5 : Reputation

1984

If you click on the pictures above, you can watch the two clips
Please read: https://on.ft.com/2EJX7Bv & https://on.ft.com/2EJGtSX

https://on.ft.com/2EJX7Bv
https://on.ft.com/2EJGtSX

1984 – part II

Why did EPIC pick this fight like this? > Read this analysis

1. Clearly EPIC’s approach is premeditated, including publicity in FT
2. Aim?

o App store of their own
o Better terms, i.e. lower tax by Apple
o No commission at all

3. Can Apple afford to give in / must they? > Read this analysis

ØWho are the players?
ØWhat are they playing for?
ØShould this be an antitrust question?

Fortnite, Apple, and the Fate of the Metaverse – A Game Theory Perspective


§ Game theory can help analyze strategic situations by formalizing conflicts,
taking into account reactions, identifying stable results

§ Definitions
Games: defined by players, sets of strategies, and payoff functions
Nash equilibrium: each player chooses the best strategy in answer the
opponent’s strategy

§ Prisoner’s dilemma
A useful prototype (that doesn’t always fit)
Selfish strategy is better for the individual but overall everybody loses

§ Cournot game
Quantity competition, decreasing reaction functions

Summary – so far

Sequential games
Now we look at games with sequential moves
Example: Market entry of Ryanair: Ryanair are considering to enter the
UK market, British Airways threatenRyanair to start a price war in case
of market entry

market
entry

no market
entry

Ryanair

British Airways status
quo

price
war

Ryanair
British Airways

0
1000

-500
0

400
400

no price
war

Nash-Equilibrium II

Nash-Equilibrium I

Sequential Games & Credible Threats (2/3)

Price war is not a credible threat è Ryanair will enter the
market

market
entry

no market
entry

Ryanair

British Airways status
quo

price
war

Ryanair
British Airways

0
1000

-500
0

400
400

no price
war

In this sub-game,
price war is not the
perfect strategy
for British Airways

Nash-Equilibrium II

Nash-Equilibrium I

Only Sub-Game Perfect
Nash Equilibrium (SPNE)

Sequential Games & Credible Threats (3/3)
Now: British Airways commits to a price war, e.g. by contract within
One World Alliance specifying 500 penalty if British Airways does not
start a price war after Ryanair’s market entry
è Ryanair will not enter the market

market
entry

no market
entry

Ryanair

British Airways status
quo

price
war

Ryanair
British Airways

0
1000

-500
0

400
400

no price
war

In this sub-game,
price war is the
perfect strategy
for British Airways

Nash-Equilibrium II

Nash-Equilibrium I

Only Sub-Game Perfect
Nash Equilibrium (SPNE)

– 500 = – 100

What if BA also face EasyJet, WizzAir, Norwegian etc… https://on.ft.com/352gy3B

https://on.ft.com/352gy3B

Why Cooperation?
Sometimes competition isn’t in companies’ best interests, e.g. prisoner’s
dilemma:

Sometimes companies need each other e.g. coordination game:

èIn these situations, cooperation can help avoid inefficient solutions

1 / 1 5 / 0

0 / 5 3 / 3

Advertise Don’t advertise

Advertise

Don’t
advertiseF
irm

A

Firm B
Nash-Equilibrium

5 / 4 1 / 0

0 / 1 4 / 5

Standard A Standard B

Standard A

Standard BFi
rm

A

Firm B

Nash-Equilibria

Achieving Cooperation

Problem:
How to achieve cooperation between (individual) profit maximizers?

e.g. how do you persuade a fierce competitor to avoid aggressive actions?

Mechanisms

• Complementarities

• Repeated games (with punishment for deviators)

• Commitment (aggressive or cooperative)

Complementarity
Firms with complementary products are complementors

§ IBM (hardware) and Microsoft (software)
§ BMW (cars) and Shell (fuel)

Direct competitors can also be complementors

§ Sony and Apple (Sony Music provides music content for iPod)

§ T-Mobile and Vodafone (cross-network calls)

Repeated Games

• We have so far looked at one-shot games.

• Better outcomes can arise in repeated interactions due to
social norms, reciprocity, and peer punishment.

• Behaving selfishly in one period has consequences in future
periods, so it may no longer be a dominant strategy.

From The Economy

Repeated Games – Prisoner’s Dilemma (1/2)

A sequential game: At each stage, the players play a simultaneous prisoner’s
dilemma game

Players know the mutual gains from cooperation – they may consider the following
strategies:

o Always cooperate

o Always deviate

o Tit-for-Tat (deviate as long as the other player deviates )

o Grim / Trigger (cooperate but deviate forever as soon as the other player deviates just once)

Repeated Games – Prisoner’s Dilemma (2/2)
Backward induction suggests that deviating throughout is the only rational strategy

However, in many real-world situations, where it is not exactly clear for how many
periods / stages a game is going to continue, we observe cooperation

Player B
deny confessPlayer
A

deny -1/-1 -4/0
confess 0/-4 -3/-3

First Stage Player B
deny confessPlayer

A

deny -1/-1 -4/0
confess 0/-4 -3/-3

Second-last stage
Player B

deny confessPlayer
A

deny -1/-1 -4/0
confess 0/-4 -3/-3

Last Stage

Cooperation is not a
Nash Equilibrium at

last stage

Cooperation is not a
Nash Equilibrium at
second-last stage

Cooperation is not a
Nash Equilibrium at

first stage

Repeated Games – Cooperation (1/4)
Example: Price Cartel

At each stage, N competitors can either charge the monopoly price or a lower price:
o if all companies charge the monopoly price, the overall shared payoff is $50mn
o if one company charges a slightly lower price, it serves all customers and receives $49mn
o if all companies charge lower prices, this ends in fierce competition with zero profits
The game continues with probability p

àCompanies play a grim trigger strategy: They charge low prices for all future seasons as
soon as any company charges a low price in one season

Value from deviating today (charging low price)
Payoff in this period: 49
Payoff in all future periods: 0

Value from cooperating today (charging high price)
Payoff in this period:

!”
#

Payoff in all future periods:
!”
#

Expected value: 49 + 0

Expected value:
!”
#

( $
$%&

)

Repeated Games – Cooperation (2/4)
For cooperation to be stable, it must hold:

!”
#

$
$%&

> 49 + 0

Factors influencing cooperation
Number of repetitions

With a higher probability that the game continues (p), future payoffs gain more weight which supports cooperation
Long-term expected interaction with suppliers, competitors and customers favours the development of cooperation

Importance of the future
Multiply the value from cooperation with

$

$%( !
!”#

)
(i being the interest rate) to capture the relative importance of

future profits

When future payoffs become more important (i decreases), this is favourable for cooperation

Number of competitors
The larger the group (N), the less stable is cooperation

Loss making competitors
• Have no future …

Value from
deviating

Value from
cooperating

Repeated Games – Cooperation (3/4)
Example: Danish Mobile Telephony
(Koski & Kretschmer 2003, Communications and Strategies)

• Up to 1998 TeleDanmark (TDC) and Sonofon (later
Telenor) were the only two providers in the Danish
market for mobile telecommunications
• However, the regulatory authority found that there

was “virtually no tariff competition” due to the
companies behaving as a “cosy duopoly”
• New licenses were issued to Moblix (later Orange)

and Telia
• With four players, competition increased

significantly

Repeated Games – Cooperation (3/4)
Example: Danish Mobile Telephony
(Koski & Kretschmer 2003, Communications and Strategies)

• Up to 1998 TeleDanmark (TDC) and Sonofon (later
Telenor) were the only two providers in the Danish
market for mobile telecommunications
• However, the regulatory authority found that there

was “virtually no tariff competition” due to the
companies behaving as a “cosy duopoly”
• New licenses were issued to Moblix (later Orange)

and Telia
• With four players, competition increased

significantly

Repeated Games – Cooperation (4/4)
Additional factors favouring cooperation

• Knowledge of opponent’s prior moves
• Adequate reaction is only possible if opponent’s actions can be

observed
• e.g. Danish cement industry
> government assisted collusion

• Knowledge of the others’ identity
• Correct reaction is only possible if you “recognize” your business

partners and if you can match players and histories
• e.g. DeBeers diamond cartel
> have-you-ever-tried-to-sell-a-diamond

https://www.jstor.org/stable/2950610
https://www.theatlantic.com/magazine/archive/1982/02/have-you-ever-tried-to-sell-a-diamond/304575/

Repeated Games – Axelrod’s Tournament (1/4)
Experimental tournament by Robert Axelrod 1980
Setting: Repeated prisoner’s dilemma
Goal: Maximizing payoffs (not “winning” as many games as possible)
Participants submitted a computer program containing a strategy
These strategies are played against each other in a “match” of 200 prisoner’s dilemmas

Possible Strategies:
1. Always cooperate
2. Always deviate
3. Tit-for-Tat (deviate as long as the other player deviates)
4. Grim – cooperate but deviate forever as soon as the other deviates just once

Repeated Games – Axelrod’s Tournament (3/4)

1st Tournament
oParticipants: 13 academics
oWinning strategy: Tit-for-Tat

2nd Tournament
o62 participants with knowledge of the first tournament
oWinner: Tit-for-Tat

3rd to 1000th Tournament
oComputer simulation
o Successful strategies in tournament k were used more frequently in

tournament k+1 (like in an ecological system)
oWinner: Tit-for-Tat à fastest increase, largest fraction

Repeated Games – Axelrod’s Tournament (4/4)
Features of successful strategies
Be nice
Start out by being cooperative, don’t be the first to play aggressively
Don’t allow exploitation
Answer an aggressive move by the opponent with an aggressive move
in the next stage
Forgive
If an aggressive opponent returns to cooperation, respond to the
“peace offer” with cooperation
Don’t be envious
Only absolute success counts (Tit-for-Tat never “wins” a match!)
Be unambiguous
Tit-for-Tat is a simple rule, quickly understood by others

Google & Motorola

2005 Google bought Android
2008 HTC bring first Android phone to market
2012 Google acquired Motorola for US$ 12.5bn
2014 Google sold Motorola to Lenovo for US$ 2.91bn

But, Google kept 15,000 patents

Google need Android to protect search
Android manufacturers prefer Google as a pure
complementor

https://on.ft.com/2QSjYhe

https://on.ft.com/2QSjYhe

Cooperative Commitment
Reputation building

o Make the company known as a reliable cooperator
o Make it known you treat others fairly

Signaling
o Invest in activities that signal competence and commitment
o E.g. education, marketing and etiquette

Self-binding commitment
o Make an investment that convinces potential partners that one is committed to act

cooperatively
o Add a provision in sales contracts that promises a customer that it will pay the lowest price

the seller charges any other customer (most favored customer clause)
o This way, it is costly to compete for customers with heavy price cuts

A380

1 / 4 [4, 2]

Aggressive Commitment (1/2)
Limiting options
• For many decisions, it’s useful to have lots of options

• Strategically, having fewer options can be beneficial

è Eliminate those moves which lead to unattractive equilibria

Example: Airframe Market

Nash Equilibria

A

B
[1, 4]

[2, 3]

[-2, -2]

B

Simultaneous Moves: No commitment

2 / 3

4 / 2 -2 / -2

747X 747X

A380

A380A
ir

bu
s

Boeing

Sequential Moves: With commitment

A380

747X

747X

747X

747X

Aggressive Commitment (2/2)
Bullying
Setting

Player 1 commits herself to the following strategy:

Best strategy for player 2: Always cooperate!

Problems with Bullying
o How to commit?
o Player 2 could also try to build a reputation as a bully

Player 2
Cooperative Aggressive

Player 1
Cooperative 3 / 3 0 / 5
Aggressive 5 / 0 1 /1

As long as player 2 chooses
“cooperative”

ð
Player 1 plays the sequence C, A (every
other move is aggressive)

ð
Expected gain
for player 2: 1,5

As soon as player 2 chooses
“aggressive” once ð

Player 1 continues with always
aggressive ð

Expected gain
for player 2: 1

Summary
Cooperation can help avoiding inefficient situations

Complementarity: Firms (even competitors) may offer complementary products

Repeated games
oMany conflicts resemble this situation
o Factors influencing cooperation: Time horizon, importance of the future,

number of competitors, knowledge of prior moves and identities, clustering of
good guys

o Tit-for-tat is a successful strategy

Commitment
oAggressive: Limiting own options, bullying
oCooperative: Reputation building, signaling

Readings

tEc Unit 4, CS Chapters 3 & 6, I2IO Chapters 4.3 & 8
alt. Dixit, AK, Nalebuff, BJ. 2008. The Art of Strategy, Norton Paperback,
Chapters 2 & 3.

Camerer CF, Fehr E. 2006. “When does “Economic Man” dominate social behavior?”
Science, 311:47-52.

Concepts
Commitment, Credible threats, Repetition, Backward Induction, Cooperation,
Punishment, Reputation

Questions

• Apply the concepts from this lecture to the interaction
between Epic and Apple
• Can you draw the next two moves, one for Apple another for Epic that

you expect with payoffs you expect.
• Do you think that government action could change the game?

• What are the likely implications of Boeing’s problems with the
737 Max airframe for the duopoly Airbus/Boeing?
• Do you thin there is a difference between repeated games with

sequential moves in stage games and repeated games with
simultaneous moves in stage games?
• Are cartels more likely in the city or the country-side?