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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

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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)


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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

ondemand through

theelasticities

(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)


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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.


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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 externalitieswhen a player’s 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 player’s action influence the decisions of other players.


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Classification of Externalities

In words … In symbols …


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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 R&D race choose how much to invest in R&D

  • Team members decide how much effort to exert

P

N

N

P


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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



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Summary: Game theory tools

  • Strategic interaction has the features of

  • 1. Externalities: a player’s 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


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Elasticity and strategic actions Coke vs. Pepsi

  • Qcoke = 64 – 4Pcoke + 2Ppepsi

  • Qpepsi = 50 – 5 Ppepsi + Pcoke

  • An increase in Ppepsishifts out the demand for firm

  • This decreases the elasticity.

  • By the mark up elasticity formula, Pcoke has to

  • increase.

  •  Prices are strategic complements


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Collusion with price competitionCoke vs. Pepsi

  • Do firms have an incentive to collude?

    Πcoke = (Pcoke – MCcoke) Qcoke

    Πpepsi = (Ppepsi – MCpepsi) Qpepsi

    Πcoke = (Pcoke– 5) (64 – 4 Pcoke + 2 Ppepsi )

    Πpepsi = (Ppepsi– 4) (50 – 5 Ppepsi + Pcoke)

  • If they collude, will prices rise or fall? Why?

  • What is the message for multi-divisional firms?


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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:

Π1 = (P1 – 6) (90 – 3P1 + 2P2)

Π2 = (P2 – 6) (90 – 3P2 + 2P1)

Firms’ price choke:

Pchoke/1 = 30 + (2/3) P2

Pchoke/2 = 30 + (2/3) P1

Firm’s reaction curves:

P1 = 18 + (1/3) P2

P2 = 18 + (1/3) P1

Hence, NE solves:

P = 18 + (1/3) P P = 27

Π = 1323


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Collusion with price competition: Numerical example (cont.)

Total demand as a function of a common price P :

Q = Q1 + Q2 = 180 – 2P

Firm’s price choke:

Pchoke = 90

Optimal common price:

P= (90 + 6)/2 = 48

collusion profit:

Π = (P– 6) (180 – 2P) = 3528

Then each firm’ s profit is

Π = 1764


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Elasticity and strategic actionswhen goods are complements

  • 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

Example: car and gazoline, Intel and Microsoft


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Collusion with price competition when goods are complements

  • Do firms have an incentive to collude?

  • If they collude, will prices rise or fall? Why?


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Summary: price competition

  • Substitute goods:

    • Positive externalities and strategic complements

    • Cartels are profitable…and illegal.

  • Complement goods:

    • Negative externalities and strategic substitutes

    • Cartels are profitable. Mergers are unlikely to be opposed.


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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:


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Cournot competition

  • Capacities have positive or negative externalities?

  • Π1 = ( 120 – Q1– Q2) Q1

  • Π2 = ( 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?


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Summary: Cournot competition

  • Example of negative externalities and strategic substitutes

  • Cartels are profitable. This is why they are illegal!


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Wrap up Strategic actions and externalities

  • If each player’s payoff is increasing (resp. decreasing) in the action of other players, the actions have positive (resp. negative) externalities.

  • If each player’s 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 games…Next time.


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How to reach the collusive outcome:Repeated games

Firm 2

Firm 1

Nash equilibrium for one shot play: Collusion:


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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.


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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?


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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 < 0.8

    • 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


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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


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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


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Airline Strategies Revisited

  • Again a Prisoner’s Dilemma

UA

(United Airline)

AA

(American Airline)


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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


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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


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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


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