Combinatorial Interlicense Competition:

[Efficient Spectrum Deregulation]{.smallcaps}

[Without Confiscation or Giveaways]{.smallcaps}

by

# Michael H. Rothkopf and Coleman Bazelon

## Rutgers University, Analysis Group

**Third FCC-SIEPR-NSF Conference**

**on**

**Combinatorial Auctions and Exchanges**

**Wye River, Maryland**

**November 22, 2003**

**The Problem**

### Spectrum is Extremely Valuable

####  U.S. Commercial Spectrum Worth \>\$770 Billion

#####  New America Foundation Study

### Current License Holders Have Limited Rights

***De Jure* vs. *De Facto***

### Spectrum is Used Inefficiently

#####  Wrong Purpose

**Wrong Technology**

### How Can We Fix This?

**Current Proposals**

**Spectrum Policy Task Force**

####  The "Medium Bang"

**Kwerel and Williams**

####  The "Big Bang"

**Expand Current License Holders Rights [for Free]{.underline}**

####  Many License Holders Got Licenses

**Free**

**For a Particular Use**

**For a Limited Time**

**With a Duty to Serve a Public Interest**

**FCC Reluctant to Evict (even with compensation)**

**Expanded Rights Would be a Bonanza**

**e.g., Channel 69 in Chicago**

**Why "Free" Since There Would Be an "Auction"?**

**Selling with no way to remove current licensees**

**Licensees** **keep** **all** **revenue from their** **licenses**

**Licensees have** ***de facto*** **veto** **over their** **licenses**

**May** **have** ***de facto*** **veto** **over** **nearby**
**licenses**

**Result: One-bidder auctions**

**Also, "Big Bang" floods the market**

### The Problems With Giveaways

#### Equity

Sen. McCain: "In the old west they robbed trains.

Now they rob spectrum."

**Political**

**Deregulation is Stalled**

**#Anti-Deregulation + #Anti-Giveaways \> Half**

### Efficiency!

**Lost Revenue Means Higher Taxes**

####  At the Margin, Taxes are Inefficient

#####  Marginal Loss \> 1/3

**Efficient Use of Government Monopoly Power:**

#####  Marg. Ineff. of Withholding = Marg. Ineff. of Taxes

**An Alternative to Giveaways:**

**(a series of annual)**

**Combinatorial Interlicense Competitions**

### Sell "Relaxation Rights" Competitively

**Usually only one bidder per right**

### 

### Intertract Competition Used in Coal Leasing

####  When there were one-bidder tracts

Basic Idea: Make One-Bidder Auction Winners Compete with Each Other

**E.g., Take bids on 20; sell only the 5 best "per unit"**

**Losers have to wait for the next sale**

### In Spectrum, Units are MHz-Pops

**Separate auctions above and below about** **3 GHz**

**Other separations** **considered**

**Use a Market-Clearing-Price (per MHz-Pop) Auction**

**Use a "Soft" Constraint on MHz-Pops to be Sold**

####  I.e., a limit with a percentage tolerance

**First, a Simple (noncombinatorial) Example**

####### A Set of Bids

# Sorted by \$/MHz-Pop

### [Bid \# \$/MHz-Pop License \# MHz-Pops (x10^6^)]{.underline}

**1 6.0121 4321 60.2**

**2 5.8327 5432 43.5**

**3 5.7511 4321 60.2**

**4 5.6330 6543 12.7**

**5 5.5112 7654 44.0**

**6 5.5081 8765 32.6**

**7 5.0423 9876 25.8**

**8 4.8899 1234 10.4**

**9 4.8001 2345 10.9**

**etc**.

######## Sell 200 (x10^6^) MHz-Pops with a Tolerance of 5%

**Bids 1and 2 win**

**Bid 3 loses (license already sold)**

**Bids 4, 5, and 6 win**

**Total MHz-Pops sold so far: 183.0 (x10^6^)**

**Bid 7would bring total MHz-Pops to 208.8 (x10^6^)**

**208.8 \< 200 x 1.05, so bid 7 wins and sets the price /MHz-Pop**

**If tolerance were 2.5%, bid 7 would lose, but still set the price**

**Bid 8 would NOT win**

**Below market**

**Some "Theorems"**

1\. If the tolerance limit exceeds the size of the largest license, then
the auction will always end with the acceptance of the marginal bid.

2\. Whether the auction ends with the acceptance or rejection of the
marginal bid, there are no price anomalies; all accepted bids offer
higher unit prices than all rejected bids.

3\. Whether the auction ends with the acceptance or rejection of the
marginal bid, the total value expressed in the accepted bids is the
maximum possible for the amount sold.

**Combinatorial Bidding**

### 

#### 

### 

### **Allow Bids on Combinations of Licenses**

### Also, Allow 

**XOR bids**

**Budget-like Constraints**

**Eligibility Constraints**

**Can a Large Combinatorial Auction Work?**

Problem: In General, the Winner Determination Problem is **NP Complete**

**Solution: Modify it**

###### Make the Constraint on the Quantity to Be Sold 

> **"Soft"**

**Apply Eligibility and Budget-Like Constraints Iteratively**

**Handle XOR bids with "Pseudo-Items"**

**The Formulation**

**Maximize Z = ~ijk~b~ijk~s~i~x~ij~y~j~**

**Subject to ~ij~s~i~x~ij~y~j~ [\<]{.underline} S,**

**~j~x~ij~y~j~ [\<]{.underline} 1, for all i,**

> **~ij~s~i~x~ij~X~jk~y~j~ [\<]{.underline} E~k~ , for all k,**

**~ij~s~i~x~ij~X~jk~b~ijk~y~j~ [\<]{.underline} B~k~, for all k,**

**0 [\<]{.underline} y~j~ [\<]{.underline} 1, for all j,**

**y~j~ integer, for all j.**

**Maximize Bid Value Sold (Not** **Revenue)**

**Subject to**

**\# of MHz-Pops to be Sold**

**Don't sell any license more than once**

**Don't let anyone buy MHz-Pops they aren't eligible for**

**Don't let anyone's winning bids exceed their limit**

**Don't sell negative fractions of a license**

**\[So far, this is an LP\]**

**& don't sell a fraction of a license**

**\[Now it is MIP\]**

**How We Can** **Solve This Problem?**

# 

### 

######### 

**Some Other Rules:**

**(In Auctions, the Devil is in the Details)**

**Rule 1.: Predictable Series of Auctions**

**Rule 2: Available Licenses and MHz-Pops Announced**

**Rule 3: Tentative Total to be Sold and Tolerance Announced**

**Rule 4: Substantial Deposits Required**

**Rule 5: Eligibility Asserted Under Oath**

**Rule 6: Any Challenge Must be Before Bidding**

(Except for Perjury Prosecutions)

#### Rule 7: If Insufficient Deposits, Tentative 

**Amount to be Sold is Reduced**

**Rule 8: Tied Bids (/MHz-Pop) Treated as One Bid**

**Rule 9: Full Payment by Winners at Once**

**Rule 10: Defaulters Lose Their Deposits**

(Bankruptcy Laws Notwithstanding)

**Rule 11: Awards at Once**

**Rule 12: Unneeded Deposits Returned at Once**

**Policy Perspective**

**Our Proposal Frees Spectrum from Constraints**

**Does not apply to "open spectrum"**

**It Frees Spectrum Gradually**

**Gradual is Good**

**Suppliers and Consumers Need Time to Adjust**

**It Uses Markets to Decide What Spectrum to Free First**

**Other proposals involve Administrative Decisions**

**It Works with Any Definition of Spectrum Rights**

**E.g., Rights requiring royalties or annual rentals**

**E.g., Full property rights**

**E.g., Limited duration rights**

**It allows bids on arbitrary combinations**

#####  Pre-auction Coasian negotiations with incumbents likely

**It Frees Spectrum without Giveaways or Confiscation**

**It is More Viable Politically**

**(Advice for Licensees on November 22:**

> **Ask not what your country can do for you.)**

**Bottom Line:**

**It is not necessary to giveaway spectrum rights to get the benefits of
eased restrictions**