Wireless Network Pricing Chapter 6: Oligopoly Pricing Jianwei Huang - - PowerPoint PPT Presentation

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Wireless Network Pricing Chapter 6: Oligopoly Pricing Jianwei Huang - - PowerPoint PPT Presentation

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Wireless Network Pricing Chapter 6: Oligopoly Pricing Jianwei Huang & Lin Gao Network Communications and Economics Lab (NCEL) Information Engineering Department The Chinese University of Hong Kong Huang & Gao ( c NCEL) Wireless

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SLIDE 1

Wireless Network Pricing Chapter 6: Oligopoly Pricing

Jianwei Huang & Lin Gao

Network Communications and Economics Lab (NCEL) Information Engineering Department The Chinese University of Hong Kong

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 1 / 29
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SLIDE 2

The Book

E-Book freely downloadable from NCEL website: http: //ncel.ie.cuhk.edu.hk/content/wireless-network-pricing Physical book available for purchase from Morgan & Claypool (http://goo.gl/JFGlai) and Amazon (http://goo.gl/JQKaEq)

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 2 / 29
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SLIDE 3

Chapter 6: Oligopoly Pricing

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 3 / 29
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SLIDE 4

Section 6.1 Theory: Game Theory

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 6 / 43
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SLIDE 5

Extensive Form Game

In extensive form games, players make decisions sequentially. Our focus is on the multi-stage game with observed actions where:

I All previous actions (called history) are observed, i.e., each player is

perfectly informed of all previous events;

I Some players may move simultaneously within the same stage. Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 21 / 43
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SLIDE 6

Market Entry

  • Firm 1 is considering entering a market that

currently has an incumbent (firm 2). !

  • Firm 1 can choose “In” or “Out”. !
  • If “Out”, firm 1 gets nothing, and firm 2 enjoys
  • monopoly. !
  • If “In”, firm 2 can choose “Accept” or “Fight”.!
  • If firm 2 accepts, then firm 1 gets a larger market

share due to a newer technology. !

  • If firm 2 fights, then there is a price war and both

firms get negative profits.

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SLIDE 7

Market Entry

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 8

Market Entry

0, 2 0, 2 2, 1

  • 3, -1

Firm 2

Accept Fight

Firm 1

Out In

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SLIDE 9

Market Entry

0, 2 2, 1 Firm 2

Accept

Firm 1

Out In

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SLIDE 10

Market Entry

Firm 2

Fight

Firm 1

Out In

0, 2

  • 3, -1
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SLIDE 11

Market Entry

0, 2 0, 2 Firm 2

Accept Fight

Firm 1

Out

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SLIDE 12

Market Entry

Firm 2

Accept Fight

Firm 1

In

2, 1

  • 3, -1
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SLIDE 13

Market Entry

0, 2 0, 2 2, 1

  • 3, -1

Firm 2

Accept Fight

Firm 1

Out In

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SLIDE 14

Market Entry

0, 2 0, 2 2, 1

  • 3, -1

Firm 2

Accept Fight

Firm 1

Out In

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SLIDE 15

Market Entry

  • Consider the Nash equilibrium

(Out, Fight if entry occurs).!

  • Firm 1 chooses to stay Out

because of firm 2’s threat of Fight.

Firm 1

Out In

0, 2 Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 16

Non-credible Threat

  • However, if firm 1 chooses In,

then firm 2 will actually choose to Accept instead. !

  • Hence Fight is a non-credible

threat.

Firm 1

Out In

0, 2 Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 17

Equilibrium Refinement

  • Principle of sequential rationality: an

equilibrium strategy should be optimal at every point of the game tree. !

  • Examine each subgame through backward

induction.

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SLIDE 18

Subgame Analysis

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 19

Subgame Analysis

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 20

Subgame Analysis

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 21

Subgame Analysis

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 22

Subgame Analysis

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 23

Subgame Analysis

Firm 1

Out In

0, 2 2, 1

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SLIDE 24

Equilibrium

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1
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SLIDE 25

Subgame Perfect Nash Equilibrium

  • A strategy profile is a subgame perfect Nash

equilibrium (SPNE) if it is a Nash equilibrium of every subgame of the original game.!

  • For market entry game, the unique SPNE is !

(In, Accept if entry occurs).

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SLIDE 26

Credible Threat

  • How to make credible threat?!
  • Eliminate choices.
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SLIDE 27
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SLIDE 28
  • Dr. Strangelove

Country A Not Attack

Attack

0, 0

Country B

Not Counter-Attack Counter-Attack

100, -200

  • , -

∞ ∞

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SLIDE 29
  • Dr. Strangelove

Country A Not Attack

Attack

0, 0

Country B

Counter-Attack

  • , -

∞ ∞

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SLIDE 30
  • Dr. Strangelove

Country A Not Attack

Attack

0, 0

Country B

Counter-Attack

  • , -

∞ ∞

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SLIDE 31
  • Dr. Strangelove

Country A Not Attack

Attack

0, 0

  • , -

∞ ∞

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SLIDE 32
  • Dr. Strangelove

Country A Not Attack

Attack

0, 0

Country B

Counter-Attack

  • , -

∞ ∞

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SLIDE 33

SPNE

  • The unique SPNE of the Dr. Strangelove game

is (Not Attack, Counter-Attack if Country A attacks).

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SLIDE 34

Extensive Form Game

Definition (Extensive Form Game) An extensive form game consists of four main elements: A set of players I = {1, 2, ..., I}; The history hk = (s0, ..., sk−1) at stage k (after stage k − 1), where st = (st

i , ∀i ∈ I) is the action profile at stage t;

Each pure strategy for player i is defined as a contingency plan for every possible history after each stage; Payoffs are defined on the outcome after the last stage.

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 22 / 29
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SLIDE 35

Extensive Form Game

Important Notations

I hk = (s0, ..., sk−1): the history at stage k (after stage k − 1); I Hk = {hk}: the set of all possible histories after stage k − 1; I Si(hk): the set of actions available to player i under a particular

history hk at stage k;

I Si(Hk) = S

hk∈Hk Si(hk): the set of actions available to player i under

all possible histories at stage k;

I ak

i : Hk → Si(Hk): a mapping from every possible history in Hk (after

stage k − 1) to an available action of player i in Si(Hk);

I si = {ak

i }∞ k=0: the pure strategy of player i.

Huang & Gao ( c NCEL) Wireless Network Pricing: Chapter 6 October 9, 2018 23 / 29
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SLIDE 36

First Mover Advantage

  • Let us look at how the first mover can have an

advantage.

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SLIDE 37

Battle of Sexes

4, 2 0, 0 0, 0 2, 4 Wife

Football Ballet

Husband

Football Ballet

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SLIDE 38

Battle of Sexes

4, 2 0, 0 0, 0 2, 4 Wife

Football Ballet

Husband

Football Ballet

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SLIDE 39

Sequential Battle of Sexes

Fo

Wife

Football Ballet

4, 2 0, 0

Husband

Football Ballet

Wife

Football Ballet

0, 0 2, 4

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SLIDE 40

Backward Induction

Wife

Football Ballet

4, 2 0, 0

Husband

Football

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SLIDE 41

Backward Induction

Husband

Football

Wife

Football Ballet

0, 0 2, 4

Ballet

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SLIDE 42

Sequential Battle of Sexes

Fo

Wife

Football

4, 2

Husband

Football Ballet

Wife

Ballet

2, 4

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SLIDE 43

Sequential Battle of Sexes

Fo

Wife

Football

4, 2

Husband

Football Ballet

Wife

Ballet

2, 4

Ballet

0, 0

Football

0, 0

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SLIDE 44

Sequential Battle of Sexes

  • Unique subgame perfect Nash equilibrium is

(Football, (Football if Husband chooses Football, Ballet if Husband chooses Ballet)).!

  • Although the equilibrium path will be

Husband picking Football and Wife picking Football, we need to specify how the Wife will pick if the Husband picks Ballet. !

  • SPNE is a contingency plan that specifies the

action at every point in the game tree.

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SLIDE 45

Sequential Battle of Sexes

Fo

Wife

Football

4, 2

Husband

Football Ballet

Wife

Ballet

2, 4

Ballet

0, 0

Football

0, 0

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SLIDE 46

First-Mover Advantage

  • Husband makes a firm commitment by

moving first. !

  • Wife thus will follow to maximize her payoff. !
  • In other games, second mover may have an

advantage, if she can take advantage of the efforts of the first mover (such as the R&D cost

  • f entering a new market).
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SLIDE 47

More Than Two Stages

  • Next we look at a game with more than two

stages.

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SLIDE 48

Nuisance Suit

  • The police confirms the defendant a small offense. !
  • The police can choose to do nothing, or sue the

defendant and ask for a small penalty.!

  • If the defendant accepts and pays the penalty, the

case is settled. The police incur some cost and receive the payment.!

  • If the defendant refuses to pay, the police can give

up and bare the cost, or go to court. !

  • When in court, the police incur additional cost but

also get benefit by winning the case. The defendant incurs additional cost.

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SLIDE 49

Nuisance Suit

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 3, 0
  • 8, -20
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SLIDE 50

Backward Induction

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 3, 0
  • 8, -20
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SLIDE 51

Nuisance Suit

Defendant

Accept

7, -10

Reject

Police

Give Up

  • 3, 0

Police

Ask for Penalty Do Nothing

0, 0

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SLIDE 52

Nuisance Suit

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Reject

Police

Give Up

  • 3, 0
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SLIDE 53

Nuisance Suit

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 3, 0
  • 8, -20
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SLIDE 54

Nuisance Suit

  • Unique subgame perfect Nash equilibrium is

((Do Nothing, Give Up if Defendant rejects), Reject if Police ask for penalty).!

  • As the police want to avoid the additional cost
  • f going to court, the defendant will take

advantage of this and refuses to pay the

  • penalty. Hence the police is better off by just

doing nothing in the first place.

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SLIDE 55

Make Threat Credible

  • Police make the threat of Go to Court credible

by paying the cost of going to court (such as the lawyer fee) even without going to court.!

  • As this cost becomes sunk before the last

stage, the police is determined to go to court.

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SLIDE 56

Nuisance Suit II

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 10, 0
  • 8, -20
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SLIDE 57

Backward Induction

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 10, 0
  • 8, -20
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SLIDE 58

Backward Induction

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court

  • 8, -20
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SLIDE 59

Backward Induction

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

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SLIDE 60

Nuisance Suit II

Police

Ask for Penalty Do Nothing

0, 0

Defendant

Accept

7, -10

Reject

Police

Go to Court Give Up

  • 10, 0
  • 8, -20
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SLIDE 61

Nuisance Suit II

  • Unique subgame perfect Nash equilibrium is

((Ask for Penalty, Go to Court if defendant rejects), Accept if Police ask for penalty).!

  • Because the police’s commitment of paying

the lawyer's fee when settlement is not successful, the defendant is ready to accept the settlement.

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SLIDE 62

Simultaneous Moves in the Same Stage

  • Multiple players can move in the same stage.
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SLIDE 63

Market Entry II

  • Firm 1 can choose to stay out or enter the
  • market. !
  • After firm 1 enters the market, both firms need

to make “accept” or “fight” decisions simultaneously, with four different possible

  • utcomes.
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SLIDE 64

Market Entry II

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1

Firm 1

Accept Fight Accept Fight

1, -2

  • 2, -1
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SLIDE 65

Backward Induction

  • First consider the simultaneous interactions in

the second stage (after entry occurs).

2, 1 1, -2

  • 2, -1
  • 3, -1

Firm 2

Accept Fight

Firm 1

Accept Fight

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SLIDE 66

Backward Induction

2, 1 1, -2

  • 2, -1
  • 3, -1

Firm 2

Accept Fight

Firm 1

Accept Fight

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SLIDE 67

Backward Induction

2, 1 1, -2

  • 2, -1
  • 3, -1

Firm 2

Accept Fight

Firm 1

Accept Fight

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SLIDE 68

Backward Induction

Firm 2

Accept Fight

Firm 1

Accept Fight

  • Accept is a strictly dominant strategy for Firm 1.!

2, 1 1, -2

  • 2, -1
  • 3, -1
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SLIDE 69

Backward Induction

2, 1 1, -2

Firm 2

Accept Fight

Firm 1

Accept

  • Accept is a strictly dominant strategy for Firm 1.!
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SLIDE 70

Backward Induction

2, 1 1, -2

Firm 2

Accept Fight

Firm 1

Accept

  • Accept is a strictly dominant strategy for Firm 1.!
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SLIDE 71

Backward Induction

2, 1 1, -2

  • 2, -1
  • 3, -1

Firm 2

Accept Fight

Firm 1

Accept Fight

  • Accept is a strictly dominant strategy for Firm 1.!
  • Unique Nash equilibrium is (Accept, Accept). !
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SLIDE 72

Market Entry II

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1

Firm 1

Accept Fight Accept Fight

1, -2

  • 2, -1
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SLIDE 73

Market Entry II

Firm 1

Out In

0, 2

Firm 2

Accept

2, 1

Firm 1

Accept

slide-74
SLIDE 74

Market Entry II

Firm 1

Out In

0, 2

Firm 2

Accept Fight

2, 1

  • 3, -1

Firm 1

Accept Fight Accept Fight

1, -2

  • 2, -1
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SLIDE 75

Market Entry II

  • Unique subgame perfect Nash equilibrium is

((In, Accept if entry occurs), Accept if entry

  • ccurs).
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SLIDE 76

Market Entry III: niche Choice

  • The third type of market entry game. !
  • Two niches in the market: large and small. !
  • Example: two types of customers.!
  • After entry, both firms need to decide

simultaneously which niche to compete in.!

  • Small niche is not profitable.!
  • Choosing the same niche leads to price war.
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SLIDE 77

niche Choice

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 78

Backward Induction

  • First consider the simultaneous interactions

after entry occurs.

  • 6, -6
  • 1, 1

1, -1

  • 3, -3

Firm 2

Small Niche Large Niche

Firm 1

Small ! Niche Large ! Niche

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SLIDE 79

Backward Induction

  • First consider the simultaneous interactions

after entry occurs.

Firm 2

Small Niche

Firm 1

Small ! Niche Large ! Niche

  • 6, -6

1, -1

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SLIDE 80

Backward Induction

  • First consider the simultaneous interactions

after entry occurs.

Firm 2

Large Niche

Firm 1

Small ! Niche Large ! Niche

  • 1, 1
  • 3, -3
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SLIDE 81

Backward Induction

  • Due to symmetry, we have two Nash

equilibria.

  • 6, -6
  • 1, 1

1, -1

  • 3, -3

Firm 2

Small Niche Large Niche

Firm 1

Small ! Niche Large ! Niche

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SLIDE 82

Backward Induction

  • Due to symmetry, we have two Nash

equilibria.

  • 6, -6
  • 1, 1

1, -1

  • 3, -3

Firm 2

Small Niche Large Niche

Firm 1

Small ! Niche Large ! Niche

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SLIDE 83

Backward Induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 84

Backward Induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 85

Backward Induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 86

SPNE I

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 87

Backward Induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

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SLIDE 88

Backward Induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-89
SLIDE 89

SPNE II

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-90
SLIDE 90

niche Choice

  • Two subgame perfect Nash equilibria!
  • ((Out, Small niche if entry occurs), Large niche if

entry occurs).!

  • ((In, Large niche if entry occurs), Small niche if entry
  • ccurs).!
  • Can we further eliminate one of the SPNEs?
slide-91
SLIDE 91

SPNE Refinement

  • Backward induction can not help.!
  • We can use forward induction:!
  • A player assumes that all previous actions are

rational when he makes a decision.

slide-92
SLIDE 92

niche Choice

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-93
SLIDE 93

Forward induction

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-94
SLIDE 94

Elimination of NE

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-95
SLIDE 95

Unique SPNE

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-96
SLIDE 96

Unique Equilibrium

Firm 1

Out In

0, 2

Firm 1

Small Niche Large Niche

  • 6, -6
  • 3, -3

Firm 2

1, -1

  • 1, 1

Small ! Niche Large ! Niche Small ! Niche Large ! Niche

slide-97
SLIDE 97

niche Choice

  • Using forward induction, we obtain the

unique equilibrium ((In, Large niche if entry

  • ccurs), Small niche if entry occurs).!
  • Forward induction is less used than backward

induction due to some tricky issues.