Techno - Economics & Policy Program

Techno - Economics & Policy ProgramP

2004 ITS conference

Optimal Spectrum Policy :A Real Option and Game

Theoretic Approach

Seoul National UniversityPh. D. Candidate

Tae-Ho Lyoo2004. 9. 6.

E

Techno - Economics & Policy ProgramP

Seoul National University

E

..CONTENTSCONTENTS ……

..

Introduction Methodology

Model

Illustrative application Market background

Policy implications

Q & A

Real option approach

Game theoretic approach

Firm’s perspective

Social welfare’s perspective

Analysis and results

Future works

Techno - Economics & Policy ProgramPE

..IntroductionIntroduction

Introduction

……..

Methodology

Model

Application

Implication

Future works

References

Q & A

Increasing need

Motivation

Indispensable source for commercializing the ICT

New services : wireless local loop, broad wireless local loop

Valuation of spectrum bandwidth

Limited spectrum resourceTechnology approach → policy approach

To optimally distribute the spectrum

Stationary method → dynamic method

Allocating new spectrum bandwidth

Redistributing bandwidth



.. ……

..MethodologyMethodology

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A

Traditional valuation methods

• future revenue • invested cost • similar transaction

• focus on the • pretty easy • tradable price can expected cash flow be calculated

• can be subjective • not regard the • difficult to find similar • parameter error future revenue cases

concept

merit

demerit

methods income approach cost approach market approach

• patent right • atomic reactor • corporeal property • trademark right • power plant • real estate• royalty contract • business practical • franchise• license

applications



.. ……

..

Dynamic changes of business circumstances

Importance of understanding uncertainty

Managers are passive

Investments are now-or-never decisions

DCF (discounted cash flow) disadvantages

Real option approach Consider management flexibility

Added information, reduced uncertainty

Consider strategy variation

Commercialization

MethodologyMethodology

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



.. ……

..

R&D

zero G(lose X)

+GV<K

save Klose X

V>Kspend K

success

failure

go

stop

X : R&D expenditure, K : commercialization cost at t

V : discounted cash flow at t

0 tτ

MethodologyMethodology

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A


Source : Ottoo, R. E ,1998


.. ……


(s)( (s)) should be interpreted as the probability that firm 1(2) chooses row(column)1 in the matrix game

Repeat game(F(Y(m)),L(Y(m)))

(L(Y(m)),F(Y(m)))(M(Y(m), M(Y(m)))

21 ( )m2 ( )m

11 ( )m

1( )mfirm1

firm2

Simple strategy for player i in the game starting at time t is a pair ofreal-valued functions ( , ) iG i

(s) is the cumulative probability that player i has moved by time s given that both players have not moved before time s

iG

(s) measures the intensity of atoms in the intervals[s, s + ds]. i

1 2

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



.. ……


The mixed strategies equilibria for the low cost firm

M : monopoly, L : leader group, F : follower group

0 if ( )

1 if

0 if

( ) if

1 if

Ll

Ll

Ll

L Fh hl l l

h h

Ll

t TG t

t T

t T

L Ft T t T

L S

t T

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



.. ModelModel ……

..

Firm’s perspective Firms are non-homogenous

Firms are risk neutral with constant discount factor r

Each firm has lower operational cost than the other for the same investment

Demand function is assumed as a linear function

Sunk cost to adopt the new technology equals I

Profit flow of firm i

Y(t) follows a geometric Brownian motion process

( )YD Q

( ) ( ) ( ) ( )dY t Y t dt Y t dw t

P a bQ

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

is a dividend yield, is a operating cost of high cost firm, is a operating cost of low cost firm, and is the positive root of equation

Follower threshold for the high cost firm, hFY

* 12

1

9

1 ( 2 )h

Fh l

b IY

a c c

hc lc1

21( 1) ( ) 0

2r r

Follower value of the high cost firm

12 *

*

2

( 2 )if

9( )( 2 )

if9

hhh l F

FhF

h

hh lF

a c c Y YI Y Y

b YF Ya c c Y

I Y Yb

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

*lMY

Follower Strategy of timing to invest

Leader value for the low cost firm

*inf( | ( ) )hF FT t Y t Y

12 2 2 **

*

2*

( ) ( 2 ) ( )if

4 9 4

( 2 )if

9

hhl h l l F

FhF

l

hh lF

a c a c c a c YY YI Y Y

b b b YLa c c Y

I Y Yb

Leader threshold value* *min( , )h l

L MY Y

is the value of making high cost firms values as like this *hLY Y h hL F

is the monopolistic threshold value *l

MY

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

*lMY

Social welfare’s perspectiveIf an amount is added to capacity, a cost equal to is incurredtQ tI Q

Social planner’s objective function is

0( ) t rt

t t tt

YU Q e dt I Q e

Let denote the maximized value of the objective function

1( , ) ( ) ( ) /W Q Y B Q Y YU Q

( , )W Q Y

The first term is the value placed by society on its options to expand this industry

The second term, is the sum of the values in place of all the installed units.

1

1 1 11 11 1

'( )'( ) ( 1) /

U QB Q I

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

*lMY

Maximized value of the objective function

1

0

1

1

( , ) ( , )

( , ) '( ) /

( , ) '( )

( ) '( )1

Q

Qv q Y dq f q Y dq

v Q Y YU Q

f Q Y B Q Y

Y Q U Q I

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



.. ApplicationApplication ……

..

Diverged, personal multimedia service

Digital Multimedia Broadcasting (DMB)

Enabling CD-quality audio and seamless video even in vehicle or train

Terrestrial DMB

Analogue 1 channel → TV 3 channels, FM 9 channels

Satellite DMB

Can offer 39 channels of quality multimedia entertainment

Use VHF channel 8(80~186MHz), 12(204~210MHz)

Anytime, anywhere

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

A company has a plan to begin and offer multimedia services late on Sep. 2004. They had already applied to the ITU for satellite orbit registration, and allowed to use the bandwidth from the region of 2.630~2.655GHz. They successfully launched the world's first satellite for DMB to the blast-off site on March 2004. Its launch has great significance in securing a leadership role in the satellite DMB market. Recently, government announced that they distributed the bandwidth for satellite DMB to S company for 12 years with a price of 7.2~8.5 billion won

Market background

Another important company in satellite DMB business in ROK, K company wantsto take part in the satellite DMB business. By the way they are hesitated to make a decision thoroughly, because there is so much uncertainty including their own company’s issue, satellite DMB business’s environment, and its uncertain policies.

ROK government has not yet made a decision to select DMB service providers, and complete the revision of DMB-related broadcasting laws. Therefore, S company has not yet obtained any preliminary business license from the government. So the timing of S company’s satellite DMB service launch this year is not certain due to the delay in revision of the Korean Broadcasting

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

category Frequency Bandwidth remarks

Satellite DMB2603~2630MHz2535~2655MHz

25MHz Among 120MHz

Terrestrial DMB VHF 12 Ch. 6MHz When allocating ch. 12

Satellite radio12~14GHz

4~6GHz306MHz

6 Broadcasting junction 27MHz4 communication junction 36MHz

Accessible Domestic DMB bandwidth

Operator position, business participation limit, accessiblenumber of channels, operator selection method, number of operators, timing of operator selection, and its standardization problems

Issues in satellite DMB business

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

r

c

Parameters S company K company

I 162,000 162,000

0.0423 0.0423

0.0448 0.0448

462 562

0.37345 0.37345

0.1654 0.1654

Assumption and dataSet satellite DMB business as an asymmetric duopoly market

Asymmetric is derived from the different operating cost

Data (million won, $1 = 1200 won)

, is estimated by using the data of NATE service’s monthly subscribers

Data’s period is 2001.12~2004.5

Parameters are estimated by MLE

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

Data categories Value

Terminal equipment 500,000~600,000

First year’s number of subscribers 450,000~500,000

Monthly fee 12,000~15,000

Subscription fee 20,000

Data for inverse demand function (people, won)

1,562 24.72P Q

The inverse demand function is set such as

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

Results

-100,000

0

100,000

200,000

300,000

400,000

500,000

1.1 1.6 1.5 2.1 2.2 3.1 4.0 4.4

Fh(Y<YF*)

Fh(Y)(Y>=YF*)

Ll(Y<YF*)

Ll(Y>YF*)

* 3.37129hFY

FirmValu

e

Y Value

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A


*

*

*

*

( )

( )

( )

( )

Fh h

Fh h

Fl h

Fl h

F Y Y

F Y Y

L Y Y

L Y Y



..

reaches value, high cost follower has an incentive to enter the market Y h

FY

The time of reaching value is . Its value is 37 months later

hFY *inf( | ( ) )h

F FT t Y t Y

If we assume a monopoly

1

1

21

1

2

12

1

( )if

4( )

( )if

44

1 ( )

lMM

l M

lM

Ml

a cYY Y Y

bM Y Y

a c YI Y Y

bb I

Ya c

is 1.003MY

In the region of , the value is higher than the low cost leader firm’s value

MY Y

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

Threshold value for low cost firm’s investing timing

-10,000

-5,000

0

5,000

10,000

15,000

20,000

0.0 0.2 0.4 0.6 0.8 1.1 2.1

계열1

계열2

Y Value

*

*

( )

( )

hh F

hh F

F Y Y

L Y Y

Leader threshold value = 0.79503

Firm value

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A




..

Low cost leader enters into market, when reaches 0.7950

Social welfare value, calculated at the , produces million won

If the initial value of is below 0.7950, neither firm will invest

Y

Y

The low cost leader enters the market with the current demand

At the ,the social welfare value is million won hFY 61.4181 10

Option value( )has more portion than the value in place of all the installed units in total value

59.3543 10

Bigger than the sum of each firm’s value at the hFY

* *

5| | 111,976 + 325,068 = 4.3704 10h hF F

l hY YL F

In the case of monopoly

lMY

48.6162 10

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



..ImplicationImplication ……

..

If we do not consider the option value, the result can be opposed to that. Without considering of the option value the firm’s value would be underestimated

The value of is 3.37129, and the time of reaching value is 37 months later.

hFY h

FY

By comparing a social welfare value in monopoly with a value in duopoly, policy maker has to let the follower enter into market to maximize the social welfare.

Can be in a better position than other country without spectrum bandwidth valuation tool

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



..Future worksFuture works ……

..

Policy maker can help each firm to achieve that level of operating cost by setting some policy such as using some equipment altogetherto reduce an operating cost.

Find the relationship between the quantity of usage bandwidth and operating cost to calculate the optimal operating costs

Find the optimal number of satellite DMB business operators without the assumption of duopoly,

Using a compound option, a comprehensive analysis of thebandwidth with the other services will be an essential issue for policy makers

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



.. ReferencesReferences ……

.. A. Dixit and R. S. Pindyck, Investment Under Uncertainty, Princeton University Press, Princeton, N. J., 1994.

S. R. Grenadier, “Option Exercise Games: An Application to the Equilibrium Investment Strategies of Firms”, Review of Financial Studies, vol.15, Summer 2002, pp. 691-721.

S. R. Grenadier, “Option Exercise Games: The Intersection of Real Options and Game Theory”, Journal of Applied Corporate Finance 13, 2000, pp. 99-107

K. J. M. Huisman, Technology Investment: A Game Theoretic Real Options Approach, Kluwer Academic Pub., Boston(MA, USA), 2001

Ottoo, R.E., 1998, “Valuation of Internal Growth Opportunities : The Case of a Biotechnology company,” The Quarterly Review of Economics and Finance 38, 615-633

R. S. Pindyck, “Irreversible Investment, Capacity Choice, and the Value of the Firm”, AmericanEconomic Review 78, pp. 969-985

H. T. J. Smit, “Infrastructure Investment as a Real Options Game: The case of European Airport Expansion”, Financial Management, winter , pp. 5-35, 2003

E. Schwartz, L Trigeorgis, Real Options and Investment under Uncertainty: Classical Readings and Recent Contrbutions, MIT Press, Campridge, MA., 2001

Dastidar, K.G.,2003, “ On Stackelberg Games in a Homogeneous Product Market,” European Economic Review

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A



Q & AQ & A.. ……

Introduction

Methodology

Model

Application

Implication

Future works

References

Q & A


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