## Spectrum Buyouts

A Proposal for the Transition to Open Spectrum

Nobuo Ikeda

Research Institute of Economy, Trade and Industry (RIETI)

Phone: +81-3-3501-8286

### E-mail: <ikeda-nobuo@rieti.go.jp>

Abstract

> To remedy the stalemate of spectrum policy, regulatory reforms are
> being proposed to assign exclusive rights to spectrum. Such reforms
> are harmful because wireless LANs enable far more efficient
> communications by sharing a wide band. So it would be better to open
> the spectrum as *commons*, instead of dividing it into narrow bands. I
> propose a system of *spectrum buyouts,* by which the government would
> take back spectrum from incumbents and reopen it for use without a
> licensing requirement. The prices of these reverse auctions would be
> much cheaper than that of ordinary spectrum auctions.

# 1. introduction

## 

In November 2002, the Federal Communications Com-mission (FCC) published
a report written by the Spectrum Policy Task Force (SPTF). Summarizing a
half year of extensive research and discussion, the report is indeed
impressive in its deep understanding of digital wireless technologies
and its call for bold reforms. Particularly noteworthy is the FCC\'s
commitment to depart from the *command and control* approach that
regulates usage by licensing. It is also remarkable that the FCC
recognized the efficiency of the *commons* approach, which shares a wide
band and enables the overlay usage of spectrum by different kinds of
terminals.

However, the SPTF\'s conclusion is a half-hearted compromise between the
commons model and the *exclusive rights* model, according to which
incumbents can sell and buy their spectrum on secondary markets. SPTF
insists that this "market-oriented" approach is more efficient than the
commons approach for the band in which "scarcity is relatively high and
transaction costs associated with market-based negotiation of access
rights are relatively low" (FCC 2002: p.38). They claim that spectrum is
scarce below 5 GHz because of its propagation characteristics and "high
level of incumbent use."

Scarcity cannot be the justification for property rights. Roads, parks
and streetlights, for example, are all supplied as commons even though
they are scarce. In standard economics, a resource is efficiently
allocated as private goods if its consumption is *rival* (the marginal
cost of consumption is large) and its supply is *excludable*
(externality is small). In principle, the externality of resources can
be internalized by dividing common resources and assigning property
rights to the parts, which can be priced and allocated efficiently by a
market mechanism (Coase 1960).

The externality of common resources is often so large that they cannot
be excluded without destroying value. Such an example is ordinary road
traffic; the road is rival because traffic jams will take place if too
many cars are on he road, but it would be inefficient to exclude each
car by building fences on the road. It is enough for each car to drive
while avoiding other drivers. The exclusive-rights model of spectrum
management is similar to such a "fence-on-the-road" approach.

"Transaction (excluding) costs" are not given exogenously, but
determined by market structure, regulation, and technologies adopted in
the band. Exclusion is needed only in so far as the spectrum is
separated by frequency. If terminals are intelligent, they can allocate
spectrum dynamically by identifying each other's signals without
exclusion, as we shall see later. In fact, alleged scarcity and
transaction costs are *created* by old technologies and poor spectrum
management based on exclusive rights. Therefore it would be circular
logic to justify exclusive rights by the scarcity that is created by
exclusive rights.

# 2. Open Spectrum

## Is Spectrum a Scarce Resource?

The auction was hit upon as a mechanism for allocating spectrum
efficiently, but it was based on the dubious assumption that the
spectrum is a scarce resource that the government has the right to
allocate. "\[I\]s the spectrum the government's to sell in the first
place?" asks Noam (1998: p. 771), "Could the state sell off the right to
the color red? To the frequency high A-flat?" He cited the licensing of
spectrum as a violation of the freedom of the press. To understand this
problem, it is necessary to distinguish *frequency* from *spectrum*.
Frequency is not a resource but a *parameter* used to modulate original
data (baseband) into radio waves, so it cannot be scarce any more than
amplitude and phase are (Benkler 1999).

In radio communications, transmitters modulate basebands into airwaves
by mixing them with carriers of a specific frequency and send the wave
in radial form. Receivers identify radio signals by tuning in to the
desired frequency and filtering out other frequencies. When basebands
are modulated into radio waves, they are distinguished by the
frequencies of their carriers. Sending multiple signals on the same
carrier causes interference. Therefore interference is not a problem of
scarcity but rather a result of *confusion* by receivers that cannot
distinguish signals from noise (Reed 2002). So a frequency can be used
by multiple users if their receivers can identify signals.

On the other hand, spectrum has limited capacity. According to Shannon's
Channel Capacity Formula, the channel capacity *C* (bits per second) is
limited by the bandwidth, *B* (Hertz):

*C = B log~2~ (1+S/N),*

where *S* is the power of the signal (in watts), and *N* is the noise
level (W/Hz). In analog radio, as it is impossible to distinguish
signals of the same frequency, spectrum should be divided into small
portions to avoid interference. And, since *N* is given physically, the
only way to do this is to magnify *S* to discern signals from noise.
Thus radio signals are sent in narrow bands and at high power to large
areas. If *B* is divided into small portions of equal size, *b~1~,
b~2~,...b~n~* and allocated to each licensee, each licensee can get at
most *C/n* of capacity. The inefficiency of this *high power and narrow
band* radio system did not matter when radio equipment was very
expensive and a small part of the spectrum was utilized, but it is
posing serious problems today.

Cellular phones depend on the circuit switching in which each user
occupies a band exclusively even if no signals are transmitted. A
digital wireless technology called *packet radio* extends *B* by sending
different packets in a band. Because packets are identified
individually, interference can be avoided even if multiple signals are
carried in the same frequency. Spectrum is used efficiently by
*statistical multiplexing*, which levels traffic in a wide band. As
average traffic usually represents a very small portion (less than 10%)
of the maximum capacity, if 100 users share a bandwidth of 20 MHz, more
than 2 MHz is available for each user on average. This is obviously more
efficient than allotting 200 kHz across 100 users.

If *B* is large, it is not necessary to magnify *S* to increase *C*.
Lowering power makes it possible to multiply spectrum by establishing
many stations. This *low power and wide band* system makes digital radio
more efficient than traditional broadcasting systems. The problem is
thus not the *scarcity* but the *efficiency* of spectrum usage.
Therefore, bandwidth can be better utilized as commons*,* shared by many
WLAN terminals. If a wide band can be shared by many users identifying
signals packet by packet, this will be much more efficient than dividing
spectrum into narrow bands and selling them to individual users.

A packet radio technology called *spread spectrum* has been widely
adopted to send various packets in a band while avoiding interference.
In the direct-sequence spread spectrum (DSSS) adopted in WLAN,
transmitters multiply original signals (baseband) by *pseudo-noise*
(encryption key) and spread the resulting signals into thin waves over a
wide band using weak power. Receivers decode the airwaves by inverse
spreading, in which the signals are multiplied by the inverse
pseudo-noise. By multiplying and dividing the baseband by the same
number, this process recovers the desired data but scatters the noise
thinly to allow its elimination by filters.

Thus it is not necessary to separate frequency to prevent interference.
A number of users can use full bandwidth by multiplexing and identifying
individual packets by their spread codes. Spread-spectrum technology was
invented during World War II to prevent interception and electromagnetic
jamming of military communications. It was later adopted for
communications in the unlicensed band (2.4 - 2.5 GHz) to prevent
interference from other devices such as microwave ovens. This band is
called the ISM (Industrial, Scientific, and Medical) band, because it
was originally released for unlicensed use by hospitals, factories, and
so on, rather than for communication purposes.

WLAN technology, standardized in the 802.11 Committee of the Institute
of Electrical and Electronics Engineers (IEEE), initially attracted
little attention because its speed was only 2 Mbps. But after the
enhanced mode IEEE 802.11b (Wi-Fi) was standardized in 1999, WLAN
exploded; within a few years the number of users worldwide grew to more
than 30 million (2002 figure). This is because 802.11b realized up to 11
Mbps (3-4 Mbps on average) by sharing the wide ISM band (22 MHz per
channel)[^1]. In contrast, the speed of data communications in current
2-G mobile telephones is around 10 kbps due to bandwidth limitations.
For example, the PDC adopted in Japan allocates only 25 kHz (12.5 KHz in
"half-rate" mode) per user.

## Multiplexing by Space, Time, and Power

The method of multiplexing airwaves for many users is not limited to
frequency. Shannon's Formula represents the limit of capacity in a given
place, but it can be extended by multiplying stations because different
users can use the same band repeatedly in separate places. This is the
cellular technology by which mobile telephones enhanced bandwidth over
traditional usage. The WLAN band is separated into a number of channels,
which are allocated to each low-power station. As shown in Figure 2,
channel A can be used repeatedly by dividing an area into many
*microcells* in which each user can utilize full capacity without
interference from other terminals. If the band is wide enough to allow
division into many channels, theoretically, the capacity can be
multiplied infinitely by dividing an area into an infinite number of
cells.

Of course, the overhead cost of connection between base stations will
limit the number of cells in reality. But if they can be connected by
wireless networks, this cost could be reduced. For WLAN terminals to be
used as base stations in *ad hoc* mode, completely distributed multi-hop
networks called *wireless mesh*, which link terminals to each other
directly, can be built by WLAN terminals. If the price of WLAN chips
falls to several dollars -- as is likely in a few years -- they will be
incorporated into a wide range of devices that can communicate with each
other.

In this regard, WLAN is even more revolutionary than wired Internet.
TCP/IP is characterized by the architecture referred to as End-to-End
(E2E), which means that the communication is controlled only by senders
and receivers. In the wired Internet, however, routing and addressing
are mostly performed by Internet Service Providers (ISP) because
networks are built on the telephone-type topology. WLAN has
deconstructed the centralized architecture and enabled completely
decentralized E2E structures physically. Such *ad hoc networks* have
been built throughout the world by volunteer organizations.

Public networks can be built by linking local wireless networks called
*hot spots* in restaurants, hotels, airports, and so on. But the quality
of the 2.4-GHz band is unsatisfactory. Industrial dryers, medical
equipment, and different types of communication terminals such as
Bluetooth interfere with WLAN. And the bandwidth (less than 100 MHz for
4 channels simultaneously) would not be sufficient if many operators
built base stations in the same place. The quality of the 5-GHz band is
higher than that of the 2.4-GHz band, although the higher the frequency
(i.e., the shorter the wavelength), the heavier the attenuation, and the
more vulnerable communication becomes to obstacles.

In the United States, 300 MHz is available within the Unlicensed
National Information Infrastructure (U-NII) band at 5-GHz band. The
European Union is planning to open 580 MHz for HiperLAN without a
licensing requirement, which can be divided into more than 25 channels
in which up to 54 Mbps can be transmitted in each channel with IEEE
802.11a. In Japan, however, there is no unlicensed outdoor band at 5
GHz; only 160 MHz is available by license and 100 MHz is available
indoors without a license.

There is another dimension by which we can utilize spectrum efficiently:
time. For example, meteorological radars occupy 5.25-35 GHz, but they
use the band for only a few minutes per hour. If other terminals can
sense the radar waves and stop using the channel while the radar
working, they can work together in a channel. Such adaptive
technologies, known as *agile radio,* have been standardized and
implemented into some 802.11a chipsets. Dividing bandwidth by time,
these technologies enables WLAN base stations to coexist with other
terminals in a band and realize much more efficient use of idle
spectrum. For example, 300 MHz of the UHF band is allotted to TV
stations, but less than a half of it is used in Japan. So if WLAN
terminals equipped with cognitive radio technologies can detect vacant
channels and use them, more than 100 MHz of spectrum can be "created."
If such *overlay* usage is allowed in all bands, available bandwidth
will be so large that its allocation would not be necessary.

Software-Defined Radio (SDR) will make such adaptation even easier by
changing physical layers by software, just like applications for PCs.
And *smart antennas*, combining various antenna elements with a single
processor, can change the transmission/reception mode in response to the
communication environment. If a channel is occupied by 802.11a, other
terminals can change its modulation to 802.11a by SDR. To deploy SDR,
however, regulatory reforms will be necessary: the present Radio Act
bans non-standardized communication devices by certification of
equipment, but if communication is performed by software, it would make
no sense to certify the equipment.

There is yet another dimension of multiplexing: power. Part 15 of the
Code of Federal Regulations defines the admitted noise level for
unlicensed devices. Ultra-Wide Band (UWB) is the technology to use such
very weak signals that cannot be distinguished from the radio noise
generated by TVs, computers, and hair dryers. In contrast to the
conventional radio technology that modulates baseband with a carrier
(sine curve), UWB modulates the baseband with very short pulses (less
than a nanosecond). This technology realizes high-speed transmission (up
to 500 Mbps) by emitting pulses in a wide band, over a frequency range
of several GHz. Since their waveforms are completely different from
those of conventional radio waves and are emitted at very low power
levels, advocates of UWB claim, the system will make overlay use
possible over all bands without interference. In fact, however,
interference was found in experiments conducted by the FCC. In February
2002, the FCC authorized UWB with very conservative restrictions for its
band (above 3.1GHz) and with weak power. Therefore, for the time being,
use of UWB will be limited to indoor use.

## Regulatory Reforms

These radically new technologies are demanding a "new spectrum policy
paradigm" according to the FCC Chairman Michael Powell (Powell 2002). To
cope with these changes, Noam (1998) proposed a reform named *open
access*. If you allocate bandwidth dynamically, this will be far more
efficient than the current system of static allocation. If demand is
lower than capacity, everybody can access bandwidth freely. If demand
exceeds capacity, a "clearing house" charges fees for wireless traffic,
acting as a tollbooth. It is much harder to charge for airwaves than for
cars because the former do not pass through specific gates, so this
proposal has been regarded as unrealistic. However, digital technologies
such as spread spectrum have now rendered this idea feasible.

If bandwidth is supplied to an extent greatly exceeding demand, open
access will become possible without fees. Even if bandwidth did not
exceed demand, the allocation of packets by spread spectrum would be
more efficient than charging for packets. Packets in the wired Internet
are stored and forwarded by routers without charge. Congestion leads to
waiting, but this is not a very serious problem in data communications
and can be overcome by widening the bandwidth. Already, we can reach up
to 108 Mbps by using two channels of 802.11a together. UWB has realized
500 Mbps and its capacity will easily extend to more than 1 Gbps.

Thus rivalry of spectrum among multiple users can be eliminated using
packet radio technologies, which increase capacity by adding stations
and terminals. If a resource is neither rival nor excludable, it should
be supplied as (pure) *public goods*. A typical example of public goods
is national security. Since there are no economic problems of resource
allocation with such services, a "market-oriented" approach does not
make sense. Instead, in the long run, the spectrum should be maintained
by public administration which makes rules and enforces them by
monitoring abuses.

"Public" does not necessarily mean "governmental." The concept of
commons is so old that it has been preserved by the social norms of the
community without any government regulation. It is the destruction of
social norms by Western companies that incurred the large-scale abuse of
tropical rainforests. Today the commons of the Internet is preserved by
hundreds of millions of users worldwide without any government control.
Standardization of radio equipment by the government has ended with the
failure of 3G. Today, such non-profit organizations (NPO) as IEEE and
the Internet Engineering Task Force (IETF) have taken over the role of
the ITU.

Of course, this does not mean that government regulation is unnecessary.
Even if there is sufficient bandwidth, interference will occur between
different physical layers. One way to prevent such interference is to
fix a physical layer (modulation) for each band; for example, 802.11b
for 2-3 GHz and 802.11a for 3-6 GHz. Some argue against unlicensed usage
because such physical regulation will impede innovation (Hazlett 2001),
but regulation is not necessary for this purpose. For example, if a
channel is occupied by Bluetooth, WLAN can use another channel by
sensing the carrier. If there is sufficient bandwidth and flexible
technologies such as agile radio are deployed, various physical layers
can coexist in different channels.

To coordinate various kinds of terminals to work cooperatively,
regulating channels, powers, frequencies, and modulations of different
terminals will be the important task of radio administration.
Traditional regulation has focused on transmitters, but it is necessary
to regulate receivers to control interference among different types of
terminals. Since digital receivers are much more tolerant of
interference than analog ones, there should be more flexible criterion
*interference temperature*, according to the FCC's term, to enable
different systems to coexist in a band.

Such regulation should be enforced not for operators but for
manufacturers because communication terminals will exist as ordinary
electronic appliances independent of operators and service providers.
The standardization can be left to the NPO, but the certification of
equipment and monitoring of abuse should be carried out by the
government. Without such supervision, unlicensed bands tend to bring
about a "tragedy of the commons" as recently evidenced by the 2.4-GHz
band. Although it is most important to supply sufficient capacity to
render abuse unnecessary and harmless, surveillance and enforcement will
have to be intensified, at least transitionally.

# 3. Reverse Auctions

## Auction Design

During the transition period, licensed and unlicensed bands will
coexist, but the criteria by which the spectrum rights are specified
should be determined not by the so-called scarcity but by the
excludability (efficiency of exclusion) of a band. Above 3 GHz, it is
pointless to exclude spectrum because there is no new technology that
depends on frequency division in that band. Exclusion might be justified
in the extremely lower band (probably below 30 MHz) where high-power
propagation is economical and no digital radio technology is likely to
be implemented. In the intermediate band, the *easement* of overlay
usage should be enforced.

Thus a strategy of transition to more efficient technologies is
necessary. As SPTF insists, spectrum policy must "provide incentives for
users to migrate to more technologically innovative and economically
efficient uses of spectrum" (FCC 2002: p.15). To achieve the goal,
however, it seems that the FCC is going to give spectrum away to
incumbents as their private property and let them use it efficiently. At
the same time when the SPTF report was published, economists at the
Office of Plans and Policy of the FCC published a working paper to
prescribe the "Big Bang auction" that would enable incumbents to sell
and buy all spectrum freely (Kwerell-Williams 2002).

Indeed this system would be politically easy to accomplish because it is
so advantageous to incumbents. However, there would exist a danger that
exclusive rights would authorize incumbents to exclude other parties'
more efficient usage. If spectrum were sold at a high price, the "owner"
of spectrum would maximize its value by monopolizing it. This is
rational behavior for individual users, but it would lead to socially
inefficient outcomes. Even worse, such a policy is irreversible; once
spectrum is given away to incumbents, spectrum commons would be lost
forever because incumbents would never open it. Easement would be harder
to enforce because incumbents would resist such "regulatory taking" of
their private property.

Legally governments can take back the spectrum when licenses expire. The
Ministry of Public Management, Home Affairs, Posts and
Telecommunications (MPHPT) of Japan announced a plan for such ruling in
November 2002. MPHPT is going to rule that, if licenses expire,
licensees must return their spectrum with compensation for the remaining
book value of their equipment. Because the term of license is five years
and the term of amortization is six years, the average licensee's
remaining value is very small. This is legitimate but difficult to
enforce. If incumbents resist, it would take a long time to evict them
by negotiation; MPHPT estimates that it would take 10 years to clear the
4-GHz band. Worse, many incumbents would refuse the "taking" of spectrum
on which their business depends and regulatory nightmare would result.

Such a problem can be resolved by breaking it down into two parts; it is
necessary to motivate incumbents to exit by compensation, but it is
harmful to admit them exclusive rights for the spectrum. So it is
advisable for the government to take back the spectrum through *reverse
auctions* and then open the acquired spectrum without a license
requirement[^2]. This mechanism can be implemented as an ordinary
procurement process by which the lowest bidder sells goods to the
government.

## Auction Design

The government should "clear" a band by taking back all the stations in
the band nationwide, but it would not be necessary to open all spectrum
because 1 GHz might be enough to supply the bandwidth for WLAN in
current use. As it is difficult to compare the value of different bands,
the government is advised to focus on specific bands. In Japan, the best
candidates for WLAN band are the 3-5 GHz used for business-use
communications and the backbones of mobile telephone networks. The
procedure would be as follows:

1.  The government announces the required minimum bandwidth, the target
    band, and the budget.

2.  Bidders register their prices to sell their spectrum via computer
    network. The bids will be known to all bidders through the network.

3.  As long as there are new bids, the government continues to lower the
    price.

4.  If no bid is registered, the auction is over.

Because simple maximization of bandwidth may result in fragmentation of
the band into many small pieces, there should be a requirement on bands;
for example, the band should be continuous more than 50 MHz. Government
can maximize the bandwidth per budget by buying the spectrum of all
stations in the band in which aggregate price is the cheapest. Suppose
the budget is 2 billion yen and aggregate bidding prices for each 10 MHz
band in 4.00-4.10 GHz are as shown in the following Table:

0.  01 02 03 04 05 06 07 08 09 10 GHz

.4 .3 .1 .8 .7 .3 .3 .4 .2 .4 .6 billion yen

Table: Bids for the band groups

In this case, government can maximize the bandwidth per budget by buying
the spectrum of all stations in 4.00-4.02 GHz with 0.8 billion yen and
4.05-4.08 GHz with 1.2 billion yen. Stated generally, the objective
function of the government is to maximize (in a given range) the total
bandwidth *W =* ∑*~i~w~i~* (*i* = 1,2,...*n*) that aggregates the
individual bands *w~i~*, within which the aggregate price *P~i~ =* ∑*~j~
p~ij~*, where *p~ij~* is the *j*th bidder's price within the *i*th band,
subject to the condition

*w~i~ ≥ r,* ∑*~i~P~i~ ≤ y*

where *r* is the required minimum continuous bandwidth and *y* is the
budget. This specific procedure is due to the requirement that the
unlicensed band should be opened in as large a block as possible. Other
requirements are possible: for example, there should not be more than
three fragmented bands or wider bands should be evaluated with some
premium.

An important characteristic of this auction is that the *aggregate*
price within each band group is compared. So the band that includes the
least number of incumbents is likely to win even if the individual
member's bid is higher than the other band. Conversely, if bidders know
the number of participants in each group, they will minimize the
aggregate price of the group to which they belong, instead of their
individual prices. To avoid such a problem, the government can
"normalize" the prices, for example, by distributing the average price
per MHz to all incumbents in the winning bands.

With such adjustments in place, bidders will have little incentive to
offer a higher price than the true value, because they bear the risk of
losing the bid, while the gain will be equally distributed among all
bidders in the group. For example, if the 4.05 GHz group raises its
price by more than 0.4 billion yen, they will be outbid by the 4.09 GHz
group. Collusion in this auction would be difficult because the
boundaries of winning bands are variable. If a group of incumbents
succeeded in lifting its aggregate prices, it could shift the boundary.

Because competition will be effective in a band where many incumbents
are evenly distributed, governments are advised to have auctions in such
well-organized bands. If these auctions are repeated, the least
populated bands will be vacated and the next least populated will be the
winner. Thus, incumbents in a densely populated band will not join the
auction in the earlier stages. As a result, we can expect the bidding
price to be roughly equal to the bidder's own valuation of spectrum,
though it would be safe to conduct experiments along these lines before
execution.

Some have argued that such an auction would be extremely costly,
referencing the prices of PCS auctions, but this would not be the case.
In an ordinary spectrum auction, an *ascending* English auction, the
equilibrium price is equal to the net present value (NPV) of the *most
efficient* use of spectrum. On the contrary, in a *descending* English
auction, the equilibrium aggregate price is approximately equal to the
opportunity cost of the *least efficient* use of spectrum on average.

The opportunity cost for a bidder includes the remaining asset value of
equipment plus the net present value (NPV) of the profit that would be
gained by using the spectrum. Usually NPV is determined by future cash
flow, terms of license, interest rates, tax, and so on. However, even if
an incumbent returns the spectrum, it can do the same business over
wireless Internet when the spectrum is opened. In such a case, the
profit would be lower because the market for the same services is more
competitive. Thus, the NPV is the discounted value of monopolistic rent
that would be smaller than the usual NPV.

Ignoring the interest rate and tax, I denote the opportunity cost of the
least efficient user *k* as *Q~k~*(*x*) *= V~k~*(*x*) *+ z~k~* where
*V~k~* is the NPV, *x* is the term of expiration, and *z~k~* is the
remaining asset value (supposed as a constant). If the government can
credibly threaten incumbents to return the spectrum, or at least if
there is uncertainty as to the duration of the license, this buyout
would be more effective. Suppose *V~k~*(*x*) is subdivided into the cash
flow *v~j\ ~*in each term. If the rule of returning is enforced in the
second term, *Q~k~*(*x*) *= v~k~ + z~k~*. If it is enforced at
probability *q* every term, the opportunity cost will be

*Q~k~*(*x*) *= v~k~* + (1*-q*)*v~k~* + (1*-q*)^2^*v~k~* +...
(1*-q*)*^x^v~k~ + z~k~.*

If *x* approaches infinity, *Q~k~ = v~k~/q + z~k~*. So the equilibrium
price *p\** will be

*p\* = v~k~/q + z~k~*.

If enforcement becomes more likely, *q* will approach 1, then *p\** will
approach *v~k~ + z~k~*; the one-term profit plus the remaining book
value of the least efficient user. Moreover, as *v~k~* is the NPV of the
most poorly operating incumbent's monopolistic rent, its value will be
very small if reverse auctions are properly designed. Even if an
inefficient incumbent refuses to join an auction, its monopolistic rent
will deteriorate when entrants do the same business over WLAN using the
opened band. Therefore, if sufficient bandwidth is opened without a
license and incumbents are rational, we can suppose *v~k~* = 0. This
result coincides with the plan of MPHPT, which takes back spectrum while
compensating for the remaining book value, that is, *p\* = z~k~*. The
difference is that the idle spectrum can be taken back right now in our
mechanism. Thus, I recommend this reverse auction as an *optional*
mechanism that incumbents can choose, together with a strong commitment
that, after the government acquires the spectrum, it will open enough
spectrum to wipe out monopolistic rents.

On the other hand, once the band is made private property, as is planned
by the FCC, *q* will approach zero and *v~k~* will increase because this
becomes profitable; therefore *p\** will be much higher and a buyout
will become more difficult. That is, the "privatization" of spectrum
makes it difficult to open it without a license. If it were possible to
suppress the rent and make spectrum commons by regulation in the end, as
Faulhaber-Farber (2002) claims, no one would buy the spectrum that would
eventually be worthless. In other words, as it is inevitable that the
value of spectrum will disappear if the wireless Internet prevails, the
NPV of every spectrum would approach zero in the long run. It would be
pointless to buy such a worthless asset or sell it at auction.

Public users cannot be bidders, but they should be compensated for the
cost of converting equipment or of exiting. Their bands should be
evaluated as the average of the nearby bidders. Another problem would be
posed by whether or not a public band should be sold; for example, the
band used by air traffic control could not be sold by the market
mechanism.

## 4. Discussion

Spectrum buyouts may arouse controversy. Some would oppose this reform
as an unfair income transfer for incumbents who are underutilizing
allocated bands. I argue that, following the Coase Theorem, it is much
more efficient to "bribe" incumbents to return their idle spectrum than
to negotiate with them over a long time. The opportunity cost of wasting
bandwidth and time would be much more expensive than the cost of buying
the band back. In my scheme, the government does not have to negotiate
with incumbents and politicians but only has to announce the reverse
auction. Incumbents will bid and reveal their valuation of spectrum, and
winners will give back their bands even if they are using them, as they
would be reimbursed for the cost of replacing their old stations and
terminals with WLAN.

Some argue that there is no need for buyouts if the overlay use of
spectrum is admitted; if every terminal could use all idle bands
dynamically, it would make no sense to reallocate spectrum at all. While
this is true, agile radio is so complicated and expensive that it has
not yet been implemented in portable terminals. To avoid interference,
agile radio terminals should store detailed data of other equipment's
characteristics such as the power, direction, and timetables of radar.
This represents not just a technical but a regulatory challenge. Overlay
use of different modulation systems in the same band requires
complicated regulation of devices, which regulators are reluctant to
enforce. UWB was at last authorized by the FCC in 2002 after 20 years of
negotiation.

It is naïve to suppose that incumbents will admit the easement of
overlay if it does not interfere the incumbent's communication. Since
massive entrance will threaten their monopoly profits, incumbents will
resist easement in their spectrum under the pretext of interference, as
evidenced in the case of UWB. In such cases, the FCC can have "overlay
auctions" to compensate incumbents for allowing easement of overlay
usage. In the long run, this would be equivalent to the reverse auctions
because incumbents will renew their equipment that can be used as
overlay. So rational incumbents would be willing to sell their spectrum
and change their stations and terminals with the auction fees.

The reverse auction is, as stated above, not a substitute for overlay
use but a complementary strategy to facilitate transition in the band
required for WLAN. Opening a clean band is obviously better than
easement, so the problem is which is the faster and cheaper method for
opening spectrum. This will depend on various factors such as progress
in radio technology, the political power of incumbents, and so forth. My
guess is that, at least in the band above 3 GHz over the next 10 years,
buyouts will prove to be the faster way. It would not be cheaper, but it
could buy precious time by "bribing" incumbents. This might work as a
middle-of-the-road solution between the commons approach, which is
economically efficient but politically difficult, and the exclusive
rights approach, which is inefficient but easy. Both incumbents and
entrants can benefit from this buyout, and we can open spectrum as
commons through a market mechanism.

Financing might be the most difficult part of this reverse auction
because the fee would be much larger than in usual procurement cases. A
simple solution would be to finance the auction through general
government accounts, in view of the fact that governments have made a
great deal of money by auctioning off spectrum to private parties. This
would cure the problem of spectrum auctions raised by Noam (1998):
auctions "tax" the communications industry and suppress investment.
Through such repayment the government can revitalize wireless operators,
which lost a great deal of money in the collapse of the bubble. It is,
in effect, a collective auction by WLAN users, so its cost is equivalent
to that of an ordinary spectrum auction, in which the winner will pass
on its costs to consumers.

Another solution, probably better suited to Japan, would be to
compensate the government's cost of reverse auctions through *spectrum
usage fees*. This would be more neutral to public finance, and raising
the fee would press incumbents to use bandwidth more efficiently or to
sell out. The present tariff of spectrum usage fees in Japan, however,
is a disincentive for efficient use of bandwidth: because the fees are
charged in proportion to the number of radio stations, more efficient
users are charged more. If the fee is charged for bandwidth, this will
offer incentives for efficient bandwidth use. As these financing methods
are complementary, governments could use them in combination.

The greatest risk might lie in having the government conduct such a
gigantic auction. It is possible that irrational behavior (as was seen
in 3-G auctions) might lead to extreme behavior and unexpected results.
If sellers rushed to sell their bands as soon as possible, the price
would be near zero, but such mistakes would be harmless for the
government. If sellers were to collude to keep the bidding high, the
government would have the option to quit. Rent seeking and collusion
would be most effective because the stakes are so high. It would thus be
necessary to perform preliminary experiments before the buyout and to
keep the procedure transparent. Further, governments would need to exit
from spectrum management after all spectrum had been opened.

# References

Benkler, Y. (1999) *Harvard J. of Law and Tech*.

<http://www.law.nyu.edu/benklery/agoraphobia.pdf>.

Coase, R.H. (1960) *J. of Law and Econ*. 3:1-44.

Faulhaber, G. and Farber, D. (2002)

> <http://gullfoss2.fcc.gov/prod/ecfs/retrieve.cgi?native_or_pdf=pdf&id_document=6513282647>

FCC (2002) *Spectrum Policy Task Force Report,*

> <http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-228542A1.pdf>

Hazlett, T. (2001) *Harvard J. of Law & Tech.*

> <http://www.aei.brookings.org/publications/working/working_01_02.pdf>

Kremer, M. (1998) *Quarterly J. of Econ*. 113: 1137-67.

<http://papers.nber.org/papers/W6304>

Kwerell, E. and Williams, J. (2002) FCC working paper,

> <http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-228552A1.pdf>

Noam, E. (1998) *J. of Law and Econ*. 41:765-790.

Powell, M.K. (2002) "Brodband Migration III"

> <http://www.fcc.gov/Speeches/Powell/2002/spmkp212.html>

Reed, D.P. (2002) ) "How Wireless Networks Scale"

> <http://www.its.bldrdoc.gov/meetings/art/art02/slides02/ree/ree_slides.pdf>

[^1]: WLAN spreads the same signal several times, so the transmission
    efficiency per frequency of 801.11b stands at 11 Mbps/22 MHz = 0.5,
    similar to that of cellular telephones.

[^2]: As a complementary mechanism to patent licensing, Kremer (1998)
    proposed a mechanism called the "patent buyout" in which the
    government buys patents from inventors through auctions and opens
    the patents to everyone.