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?