Auctioning non-exclusive mmwave licenses

Petri Mähönen, Ljiljana Simić and I recently filed comments in the Spectrum Frontiers proceeding, FCC Docket No. 14-177 (filing page, pdf, docket on ECFS). We argued that the operating and propagation characteristics of mm-wave systems mean that non-exclusive licensing – meaning in this case, a limited number of large-area licenses assigned by auction – is an appropriate middle path between exclusive large-area licensing (which may lead to under-utilization) and unlicensed (which may not provide sufficient interference protection).

To support this contention, we drew the Commission’s attention to four recent academic contributions to the wireless system research literature that suggest to us that non-exclusive mm-wave licensing is a viable option:

• Rebato et al., “The potential of resource sharing in 5G Millimeter-Wave bands” (2016), ArXiv, https://arxiv.org/abs/1602.07732;
• Gupta et al., “On the feasibility of sharing spectrum licenses in mmWave cellular systems” (2016), IEEE Transactions on Communications, http://dx.doi.org/10.1109/tcomm.2016.2590467;
• Boccardi et al., “Spectrum pooling in MmWave networks: Opportunities, challenges, and enablers” (2016), IEEE Communications Magazine, http://dx.doi.org/10.1109/mcom.2016.1600191cm;
• Fund et al., “Spectrum and infrastructure sharing in millimeter wave cellular networks: An economic perspective” (2016) ArXiv, https://arxiv.org/abs/1605.04602.

Our filing did not describe how an auction might work, but I believe it would be similar to the mechanisms I proposed for satellite constellation licenses. A clock auction could determine both the number and identity of players to be licensed, as well as their relative interference protection rights. (The latter could, I think, circumvent or at least mitigate the concern Fund et al. (2016) identified: that the leading service provider in a duopoly market prefers to share resources only under limited circumstances.)

Since economists seem to prefer ascending auctions, here’s how it could work in this case:

• Define a large number of tickets, N >> number of bidders.
• In each round, parties can bid for some number of tickets at the current price (e.g. if price in round 3 is p3, to get k tickets, bid k*p3).
• If the round is oversubscribed, i.e. there are bids on more than N tickets, the auction moves to the next round.
• The price increases in each round (p1 < p2 < p3 …) until the number of tickets bid for is equal or less than N.
• The bidders that remain at the end of the auction are the ones that are licensed. Each pays the price of the round times the number of tickets they each bid for.
• Oleg Baranov suggested to me that the auctioneer can set minima and maxima on the number of tickets any party can bid for, to prevent trivial participation and monopoly, respectively.

One can determine an interference priority stack for the licensees, if desired, by calculating dividing the tickets bought by each successful bidder (i.e., all those left standing at the end) by N. There are various ways one could use/interpret these fractions. For example, they could be used to determine who must yield to whom if there’s competition for the use of a particular communications path; or one could use the bid fractions to determine how the band is to be split if there is a concurrency conflict.

In the language of club good theory (a non-exclusive allocation resembles a club, since use of the “resource” is nonrival until some congestion threshold is crossed) the auction determines both the number of members, and the membership fee – without the regulator having to play god with club good equations to determine these parameters. (The auction payments in the above design aren't exactly membership fees, since each licensee pays a different amount for "entry.")

Update 18 September 2018

Here’s an auction mechanism that could determine both the number of members and a uniform membership fee. (Whether this mechanism will reach equilibrium is left as an exercise in auction theory, as is the design of price increments etc.)

It’s an ascending clock auction of an indeterminate number of memberships. In each round, players can choose to drop out of the auction, or buy the membership at the current round price. (Once a player has dropped out, they cannot reenter.) At the end of the round, the auctioneer calculates the total proceeds of the auction as # bidders times the round price.

Starting at a low enough initial price, the proceeds will increase from round to round initially. At some point, the price will be so high that the number of bidders starts dropping. Eventually, a round will be reached where the proceeds are less than the preceding round, and the auction stops. (Alternatively, the auctioneer could go back a step and try smaller bid increments, perhaps recursively, in an attempt to approximate the maximum more closely.) The bidders and price in the penultimate round (i.e., the maximum price reached) is the outcome of the auction. The “membership fee” is the price bid in the penultimate round.

Update 20 September 2018

Toby Youell pointed out to me that Ofcom’s 2006 sale of DECT guard band licenses was an auction of spectrum club goods; I've taken a look at how the Ofcom auction worked.