Avoiding the Bertrand Trap II: Cooperation

1
Road Map for Prices and Markets

• Real world somewhere between the polar cases of
  monopoly and perfect competition. Unfortunately,
  this is a much harder problem to solve and
  requires the techniques of GAME THEORY
• More Tools Game Theory
• Importance of Strategic Thinking
• Simultaneous Games
• Predictions ? Nash equilibrium
• Oligopoly (finite number of firms)
• Price games and Quantity games
• Implicit Collusion with Repeated Games
• Mergers
• Sequential Games and backward induction
• Leader-Follower games and First Mover Advantage
• How timing matters

Topic 10 (Session 11)
Topics 11,12,13 (Sessions 12,13,14)
2
Understanding Cost (session 3)
Revenue Understanding Demand (session 2)
Profit Revenue Cost
Pricing
Monopoly Trade off b/w high P and low Q
(session 6)
Perfect Competition Supply and entry decisions
(session 4 5)
What if we can price discriminate? (i.e.,
different consumers pay different
prices) (session 9 10)
How pricing depends on demand through the
elasticities (session 7)
Strategic Competition Solving for the NE
price and quantity competition (session 12)
How timing matters Stackelberg (session 14)
Exotic topics Strategic Demand Network
externalities and Auctions. (session 15)
Tools Games Theory (session 11)
Externalities and Strategic interaction
Collusion (session 13)
3
This Session

• Oligopolistic Markets
• Individual versus Collective action
• Strategic actions and externalities
• Compare the collusive outcome with the Nash
  equilibrium (NE)
• How to reach the collusive outcome
• Implicit collusion in repeated games
• Implicit collusion trough loyalty programs

• Key lessons
• The collusive outcome reaches higher profit.
  That is why firms are inclined to merge.
• When merging is not possible, tacit collusion
  can be reached (illegally) in repeated games.

4
Strategic interactions and externalities

• Motivating questions
• How do you react if the other firm raises its
  price?
• Does it help you or hurt you if your opponent
  raises his price?

• Definitions
• There are externalities when a players action
  affect the payoffs of other players, but the
  player takes only his own payoff into account
  when choosing his action.
• We say that the player does not internalize the
  effect of his action.
• There is strategic interaction when a players
  action influence the decisions of other players.

5
Classification of Externalities
In words
In symbols
6
Externalities
Example
N

• Housemates with different music tastes choose
  volume levels on their stereos.
• Listeners of a private but non-profit (and
  listener-supported) radio station choose how much
  to contribute to the station.
• Competing firms choose advertising expenditures
• Firms in an RD race choose how much to invest in
  RD
• Team members decide how much effort to exert

P
N
N
P
7
An Implication of Externalities
Are Nash equilibrium actions higher or lower than
those that maximize total payoffs?
Externalities
Lower In NE players do too little of the good
thing
Positive Negative
Higher Players do too much of the bad thing
8
Classification of Strategic interactions
9
Summary Game theory tools

• Strategic interaction has the features of
• 1. Externalities a players action affects
  others
• 2. Complementarities/substitutability My action
  depends on what I think others will do
• The slope of reaction curves reveals whether
  actions are strategic complements or substitutes

10
Elasticity and strategic actions Coke vs. Pepsi

• Qcoke 64 4Pcoke 2Ppepsi
• Qpepsi 50 5 Ppepsi Pcoke
• An increase in Ppepsi shifts out the demand for
  firm
• This decreases the elasticity.
• By the mark up elasticity formula, Pcoke has to
• increase.
• ?? Prices are strategic complements

11
Collusion with price competitionCoke vs. Pepsi

• Do firms have an incentive to collude?
• ?coke (Pcoke MCcoke) Qcoke
• ?pepsi (Ppepsi MCpepsi) Qpepsi
• ?coke (Pcoke 5) (64 4 Pcoke 2 Ppepsi )
• ?pepsi (Ppepsi 4) (50 5 Ppepsi Pcoke)
• If they collude, will prices rise or fall? Why?
• What is the message for multi-divisional firms?

12
Collusion with price competition Numerical
example
Two firms. Common MC 6 and following demand
functions Q1 90 3 P1 2 P2 Q2 90
3 P2 2 P1 Firms profits ?1 (P1 6) (90
3P1 2P2) ?2 (P2 6) (90 3P2
2P1) Firms price choke Pchoke/1 30 (2/3)
P2 Pchoke/2 30 (2/3) P1 Firms reaction
curves P1 18 (1/3) P2 P2 18 (1/3)
P1 Hence, NE solves P 18 (1/3) P
P 27 ? 1323

13
Collusion with price competition Numerical
example (cont.)
Total demand as a function of a common price P
Q Q1 Q2 180 2P Firms price
choke Pchoke 90 Optimal common price P
(90 6)/2 48 collusion profit ? (P
6) (180 2P) 3528 Then each firm s profit is
? 1764

14
Elasticity and strategic actionswhen goods are
complements
Example car and gazoline, Intel and Microsoft

• Let
• An increase in P2 shifts in the demand for firm
  1. This increases the elasticity.
• By the mark up elasticity formula, P1 has to
  decrease.
• ?? Prices are strategic substitute

15
Collusion with price competition when goods are
complements

• Do firms have an incentive to collude?
• If they collude, will prices rise or fall? Why?

16
Summary price competition

• Substitute goods
• Positive externalities and strategic complements
• Cartels are profitableand illegal.
• Complement goods
• Negative externalities and strategic substitutes
• Cartels are profitable. Mergers are unlikely to
  be opposed.

17
Cournot competition Cartels?

• P 150 Q MC 30
• We found that the NE quantities are Q1 Q2 40
• Act as a monopolist on the demand curve

18
Cournot competition

• Capacities have positive or negative
  externalities?
• ?1 ( 120 Q1 Q2) Q1
• ?2 ( 120 Q1 Q2) Q2
• Capacities are strategic complements or
  substitutes
• Do firms have an incentive to collude?
• If they collude, will quantities rise or fall?
  Why?

19
Summary Cournot competition

• Example of negative externalities and strategic
  substitutes
• Cartels are profitable. This is why they are
  illegal!

20
Wrap up Strategic actions and externalities

• If each players payoff is increasing (resp.
  decreasing) in the action of other players, the
  actions have positive (resp. negative)
  externalities.
• If each players reaction curve is increasing
  (resp. decreasing), then the actions are
  strategic complements (resp. substitutes).
• Understanding externalities and strategic
  interactions allow us to make conclusion
  concerning the profitability of mergers or
  cartels in price and Cournot competition.
• Externalities and strategic interactions are also
  useful to systematically compare the outcome of
  static and sequential gamesNext time.

21
How to reach the collusive outcomeRepeated games
Firm 2
Firm 1
Nash equilibrium for one shot play Collusion
22
Trigger Strategies to Enforce Collusive Outcome

• Begin by cooperating
• Cooperate as long as the rivals do
• Upon observing a defection immediately revert to
  a period of punishment of specified length in
  which everyone plays non-cooperatively
• Example
• Grim Trigger Strategy (GTS)
• Start off setting the collusive price which leads
  to a profit of 10,000 and continue to do so
  until the other firm cheats
• Then, set Nash equilibrium price forever after
• If you cheat you make 20,000 for one time period
  and then 2,000 forever after.

23
Payoffs
PV (collude)
PV (cheat)

20000
collude
10000
2000
cheat
t 1
t 2
t 3
time
Q Is (Collude,Collude) for ever, a Nash
equilibrium?
24
Tacit Collusion Weighing Costs and Benefits

• For tacit collusion to work
• Gains from cooperation must exceed net gain from
  cheating and being punished
• That is
• You would collude if PV of colluding PV of
  cheating
• 10,000 10,000/r 20,000 2,000/r ? r
• Could this condition hold?
• Key take-away point If detection is certain and
  punishment is quick,
• Grim Trigger strategy can effectively deter
  cheating and ensure collusion

25
Finitely repeated games

• Can threat and promises have an impact in a
  finitely repeated game?
• The two-time repeated game
• The three-time repeated game
• The n-time repeated game

26
Summary Repeated games

• In repeated games, there is room for players to
  make threats and promises
• A system of such threats and promises can support
  a cartel in a price competition game, provided
  that firms are patient enough and the horizon is
  infinite
• Building reputation is important
• With a finite horizon such threats and promises
  have no effect on the equilibrium

27
Airline Strategies Revisited

• Again a Prisoners Dilemma

UA (United Airline)
AA (American Airline)
28
Changing Payoffs Frequent Flyer Programs
(Loyalty Programs)

• By implementing a loyalty
• program, like a frequent flyer
• program, AA can reduce the
• incentive for UA to price Low.
• Pricing Low is no longer a
• dominant strategy for UA.

UA
AA
29
Frequent Flyer Programs (Loyalty Programs)

• The really big win comes if the
• rival imitates the frequent flyer
• program as well.
• Nash
• Frequent flyer programs raise switching costs
  changes game

UA
AA
30
Wrap Up on Tacit or Implicit Collusion

• Tacit collusion is easier to sustain when
• Repeated interaction and no finite end to game
• Trigger Strategies Loyalty Programs
• Fewer firms ? Reduces the size of temptation to
  cheat
• Interest rate low ? Increases the value of the
  future

• If in a price game
• Differentiate product
• Change payoffs through loyalty programs
• Collude implicitly through trigger strategies