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Designing Auction Mechanisms for Dynamic Spectrum Access

Mobile Networks and Applications, 2008, Volume 13, Number 5, 498-515(Impact Factor: 1.619 in 2008)

School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA(in 2008)

Shamik Sengupta and Mainak Chatterjee

Presented by: Ming-Lung Lu

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Why I choose this paper? The authors have presented an article in IEEE/ACM

Transaction on Networking, 2009. “An Economic Framework for Dynamic Spectrum Access and

Service Pricing” In that article, the authors proposed “Winner Determining

Sealed Bid Knapsack Auction” for the spectrum broker to allocate spectrum to service providers.

However, not all details of such auction were revealed in that article.

Thus it is incentive to study their previous research on auction to better understand how does the auction work.

At last, I hope that it could help me to compare the difference between auction and our proposed method.

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Outline1. Introduction2. Related work3. Auction design and classifications4. Auction design for single unit grant5. Auction design for multiple unit grant6. Simulation model and results7. Conclusions8. Comments

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Introduction In most countries, the competitive behavior of

wireless service providers (WSPs) was initiated by spectrum auctions held in 2010 and 2011.

Spectrum in the United States was auctioned through the Federal Communications Commission (FCC). For example, 824–849 MHz, 1.85–1.91 GHz, 1.930–1.99

GHz are reserved for licensed WSPs, whereas 902–928 MHz, 2.40–2.50 GHz, 5.725–5.825

GHz are free-for-all unlicensed bands. The spectrum allocations are usually long-term

and any changes are made under the strict guidance of FCC.

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Introduction (cont’d) Studies have shown that the spectrum usage is both

space and time dependent, and therefore static allocation of spectrum often leads

to low spectrum utilization. Moreover, static allocation of spectrum is inflexible.

Consider the WSPs are willing to pay for extra amount of spectrum for a short period of time if there is a demand from the users they support.

Static allocation fails to address the issue of spectrum access in such scenario.

In order to break away from the inflexibility and inefficiencies of static allocation, a new paradigm called Dynamic Spectrum Access (DSA) is being investigated [2].[2] Buddhikot M, Kolodzy P, Miller S, Ryan K, Evans J, “DIMSUMnet: new directions in wireless

networking using coordinated dynamic spectrum,” Sixth IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM), 2005, pp. 78 – 85.

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Introduction (cont’d) In DSA, spectrum bands would be allocated

and de-allocated dynamically from coordinated access band (CAB) [3]. Examples: public safety bands (764–776 MHz,

794–806 MHz), and unused broadcast UHF (Ultra High Frequency)

TV channels (450–470 MHz, 470–512 MHz, 512–698 MHz, 698–806 MHz).

These bands will be dynamically leased to WSPs on a short-term basis in addition to the statically allocated spectrum that all WSPs already have.[3] Buddhikot M, Ryan, K. “Spectrum management in coordinated dynamic spectrum access based

cellular networks” First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 2005, pp. 299 – 307.

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Introduction (cont’d) Allocating spectrum dynamically among competing WSPs raises

one important question: “how would the optimal allocation be achieved?”

With the exact value of spectrum unknown to both the seller and the buyers (WSPs), the use of auctions is a rational choice,

since the spectrum bands in the CAB is less than the usual aggregate demand from the WSPs.

The auction is for every geographic region; includes 2 different parties:

service providers (in the region) = bidders, spectrum owner = auctioneer (seller)

is conducted in a periodic manner: Spectrum would be allocated and de-allocated every auction period, which is

also known as the lease duration. At the end of the lease duration, all WSPs would release their bands and fresh

auction will be again initiated.

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Introduction (cont’d) We investigate spectrum auction mechanisms when

multiple units of spectrum are available and the demand from WSPs exceeds the available spectrum

Various auction mechanisms under different allocation constraints are studied to find WSPs’ bidding strategies revenue generated by the auctioneer

These auctions can be classified in terms of Single unit grant vs. multiple unit grant Sequential vs. concurrent Substitutable vs. non–substitutable Synchronous vs. asynchronous

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Related work Single unit auction

Most auction sites (e.g., eBay) support it. Ascending bidding continues till a winner emerges

Vickrey proved that “English” and “Dutch” type auctions yield the same expected revenue [16]. English auction = open ascending price auction Dutch auction = open decending price auction

With the emergence of spectrum markets, single unit auction models are no longer valid.

Multi-unit auctions have been used to investigate pricing policies of network resources E.g., transmission rate, bandwidth or link capacity

[16] William Vickrey. “Counterspeculation, Auctions, and Competitive Sealed Tenders,” The Journal of Finance, Vol. 16, No. 1, Mar., 1961, pp. 8 – 37.

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Related work (cont’d) In [5], how the available bandwidth within the

network should be shared between competing streams of elastic traffic is concerned. The stability and fairness of a class of rate control

algorithms are also investigated. In [6], the implications of flat pricing and

congestion pricing for capacity expansion are studied.

In [7, 8], a bandwidth pricing mechanism based on second-price auctions that solves congestion problems in communication networks has been proposed.

[5] F. P. Kelly, A. K. Maulloo and D. K. H. Tan, "Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability," The Journal of the Operational Research Society, Vol. 49, No. 3, Mar., 1998, pp. 237-252.[6] Jeffrey K. MacKie-Mason, Hal R. Varian, "Pricing congestible network resources," IEEE Journal on Selected Areas in Communications, Vol. 13, No. 7, Sep. 1995, pp. 1147-1149.[7] Patrick Maillé and Bruno Tuffin, "The Progressive Second Price Mechanism in a Stochastic Environment," NETNOMICS, Vol. 5, No. 2, pp. 119-147.[8] Patrick Maillé and Bruno Tuffin, "Multibid auctions for bandwidth allocation in communication networks," INFOCOM, 2004, pp. 54-65

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Related work (cont’d) In [12], a decentralized auction-based approach to

price edge-allocated bandwidth in a differentiated services Internet is presented.

Most works done so far on auctions are extensions of Vickrey auction with somewhat strong assumptions. The auctions are designed such that the bidders with higher

bids are always favored. But favoring higher bidders does not always necessarily maximize

the revenue. Moreover, FCC’s intention is not only to maximize but also to be fair

to the market. The objects in multi-object auctions to have a common value.

But it may not be true for spectrum auction. Because revenue generated from the same spectrum band may be

different for different WSPs.[12]Nemo semret, "Market mechanisms for network resource sharing," Ph.D. dissertation, Columbia University

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Related work (cont’d) In [9, 10], a DSA scheme in which a spectrum

manager periodically auctions short-term spectrum licenses. The spectrum is sold at a unit price. It is assumed that a large number of spectrum

buyers are present and none has enough power to influence the market clearing price. Market clearing price is the price that balances the

supply and demand. In [11], Spectrum auctioning mechanisms

under heterogeneous wireless access networks have been investigated.

[9] Rodriguez V, Moessner K, Tafazolli R (2005) Market-driven dynamic spectrum allocation: optimal end-user pricing and admission control for CDMA. In: Proc. 14th European information society technologies (IST) mobile and wireless communications summit. Dresden, June 2005[10] Rodriguez V,Moessner K, Tafazolli R (2005) Auction driven dynamic spectrum allocation: optimal bidding, pricing and service priorities for multi-rate, multi-class CDMA. In: IEEE 16th international symposium on personal, indoor andmobile radio communications (PIMRC), vol 3. IEEE, Piscataway, pp 1850–1854[11] Sallent O, Perez-Romero J, Agusti R, Giupponi L, Kloeck C, Martoyo I, Klett S, Luo J (2006) Resource auctioning mechanisms in heterogeneous wireless access networks. In: IEEE 63rd vehicular technology conference, VTC 2006-Spring, vol 1. IEEE, Piscataway, pp 52–56

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Auction design and classifications There are three important issues behind any

auction design.1. attracting bidders (enticing bidders by increasing

their probability of winning)2. preventing collusion thus preventing bidders to

control the auction3. maximizing auctioneer’s revenue

Not only big companies with high spectrum demand should acquire entire spectrum.

It is necessary to make the small companies, interested in taking part in the auction.

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Auction design and classifications (cont’d) In an auction, the auctioneer must answer couple of

questions: What is the objective of the spectrum allocator?

Apart from maximizing the revenue, the spectrum owner must also be fair in leasing out the unused spectrum bands.

What would be the pricing and market mechanisms? Fig. 1 (next page) presents the classification of auctions.

Single unit grant: bidders are allowed to get at most one unit. multiple unit grant

Sequential: spectrum bands are auctioned one after another. concurrent

Substitutable: a bidder will not care about which band(s) he gets as long as all the bandwidths are equal. non-substitutable

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Auction design and classifications (cont’d) For multiple unit grant, we only analyze the

non-substitutable bands. This is because substitutable bands under

multiple units grant is isomorphous to non-substitutable bands under the single unit grant from multiple units for the bidders. But the authors didn’t explain it! And actually the analyzed one is for substitutable

bands

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Auction design for single unit grant The structure of this section are as follows:

Sequential auction for substitutable bands Concurrent auction for substitutable bands Dominant strategy – sequential and concurrent

auction Concurrent and sequential auction for non-

substitutable bands That is, we will start from the simplest one

(substitutable) And then generalize to non-substitutable

bands.

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Common setting Terminology

Let S = {s1, s2, …, sm} be the m substitutable spectrum bands N = {N1, N2, …, Nn} be the n bidders B = {b1, b2, …, bn} denote the bids from the bidders. V = {V1, V2, … Vn} be the true valuation price of a substitutable band Thus the payoff of a bidder is

Vi – bi, if ith bidder wins 0, if ith bidder loses

We follow the seal-bid auction policy to prevent collusion. Auction among the WSPs occur periodically with the period being

the DSA period. In sequential auction, each DSA period consists of m auction round. In concurrent auction, each DSA period consists of only one auction round.

When one DSA period expires, all the bands are return to the auctioneer and the process repeats for both sequential and concurrent bids.

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Common setting (cont’d) Bidder’s behavior

We assume all the bidders in the auction to be rational such that… Losing bidders in any auction round will increase their bids by

certain amount in the next round if their bids were less than the true valuation of the bands.

Winning bidders will decrease their bids by certain amount in the next round to increase their payoff.

This continues until a steady state is reached. Note that the “ next round” seems to be the next auction process in

the next DSA period. But the authors didn’t clarify it. At the end of each auction round, the auctioneer only

broadcasts the information of minimum bid submitted in that round. This makes bidders have no smart strategy to change his bid.

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Sequential auction for substitutable bands We assume a time instance when the auction for k

spectrum bands are over and k winners have emerged. As a result, there are (n-k) bidders competing (m-k)

spectrum bands. We assume that bids from all the bidders are uniformly

distributed. The probability density function of bid can be given by

where Vmax is the maximum valuation possible of a spectrum band,

bmin is the minimum bid of all the bids submitted by the existing bidders.

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Sequential auction for substitutable bands (cont’d) Let us assume that bidder i submits a bid bi at the beginning

of (k+1)th band auction. Bidder i will win the (k+1)th band if and only if all the (n-k-1)

bidders’ bids are less than bi. The probability that any bid bj < bi can be given by

And then the probability of bidder i winning the (k+1)th band can be given by

And thus

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Sequential auction for substitutable bands (cont’d) Optimal bid analysis

We define optimal bid of ith bidder as the bid that wins a band and maximizes the pay off for ith bidder.

The ith bidder’s expected payoff is given by

To maximize Ei, we equate the first derivative of Ei to 0, i.e.,

We obtain the optimal bid for ith bidder in (k+1)th auction round as

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Concurrent auction for substitutable bands Similar to the analysis in sequential auction, the

probability of bidder i winning a band in concurrent auction can be given by

The expected payoff is given by

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Concurrent auction for substitutable bands (cont’d) To maximize Ei, we take the first derivative of

Ei and equate to 0

Solving (15), we obtain the optimal bid for ith bidder in concurrent auction as

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Dominant strategy – sequential and concurrent auction In this section we want to compare the optimal bids for sequential

and concurrent auction to study the dominant strategies for bidders. Let us consider the difference:

In the following, we consider two cases: Transient state

The learning phase where bidders have not reached the steady state and are willing to experiment with their bids.

Further we consider two cases At the beginning After k spectrum bands auctions are over.

Steady state All the bidders eventually settle down to their corresponding fixed bids After that bidders will have no extra payoff in unilaterally changing their bids.

We show that the difference is positive in every state to conclude that it is more beneficial for the auctioneer to follow the sequential auction.

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Dominant strategy – sequential and concurrent auction (cont’d) Transient state – at the beginning

The difference is give by

We know that for a bidder to win a spectrum band, the following conditions must be true:

Thus the difference is positive Optimal bid to win in sequential auction setting is more than that in

concurrent auction. Besides, with increase in m, the difference also increases. Thus increasing available spectrum bands does not benefit the

auctioneer in concurrent auction setting.

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Dominant strategy – sequential and concurrent auction (cont’d) Transient state – k bands auctioned so far

In sequential auction, bidders get the opportunity to revise their bids (m-1) times more in each DSA period.

Then in concurrent auction, minimum bid submitted would be less than that in sequential auction.

Let the minimum bids in sequential and concurrent auctions be bmin1 and bmin2, bmin2 <= bmin1.

The difference in optimal bids is

Since the difference is positive, the optimal bids in sequential auction is more than that in concurrent auction.

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Dominant strategy – sequential and concurrent auction (cont’d) Steady state reached

We assume that the auction has been run for sufficient large number of times to reach the steady state

As we assume the auction model to achieve the steady state, minimum bid submitted for both sequential and concurrent auction would be the same.

Then the difference is given as

It again shows that the difference is positive. And sequential auction is more beneficial to

auctioneer.

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Concurrent and sequential auctions for non-substitutable bands Generalize the valuation price to be:

V = {{V1}, {V2}, …, {Vn}} {Vi} is the valuation price vector of ith bidder for

all m spectrum bands, i.e., Vi = {Vi1, Vi2, …, Vim}

Let the reservation price of ith bidder for all m spectrum bands be Ri = {ri1, ri2, …, rim}

A bidder i will choose to submit bid for that spectrum band which will maximize his payoff profit: Ui = Vij – rij

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Concurrent and sequential auctions for non-substitutable bands (cont’d) It may happened that multiple bidders submit

the same spectrum bands. In such cases, the maximal bid would be

accepted. In concurrent auction, losing bidder has no

chance to revise his bid. Thus it is possible that some spectrum bands

are not allocated at the end.

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Concurrent and sequential auctions for non-substitutable bands (cont’d) Concurrent auction

Consider only one band j. If there are l bidders aim for this band j, the

revenue Revlj would be the maximum bid submitted from all these l bidders.

Then the total revenue generated from all the n bidders and m bands can be expressed as

Sequential auction The total revenue can be expressed as

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Auction design for multiple unit grant In this section, we investigate the more general case

where WSPs are allowed to win multiple unit. We map such case to the knapsack problem

There are n bidders The spectrum band available is W The strategy taken by service provider i as qi:

qi = {wi, xi} wi denotes the amount of spectrum xi denotes the bidding price

The allocation policy of the spectrum owner would be

Subjects to

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Auction design for multiple unit grant (cont’d) The proposed sealed bid knapsack auction consists of

two cases Synchronous

Bids are taken simultaneously Allocation/de-allocation of spectrum are done only at fixed intervals

Asynchronous Contrary to the attributes of synchrous The strategy taken by WSPs is generalized to

where Ti is the duration for which the spectrum amount is requested.

When bids come If the remaining spectrum is enough, directly allocate the spectrum. If the remaining spectrum is not enough, auction is initiated.

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Auction design for multiple unit grant (cont’d) Figure shows the asynchronous and

synchronous

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Auction design for multiple unit grant (cont’d) Bidders’ strategies

Let us consider a bidder j who wins in the auction Denote the optimal spectrum allocation as M Assume a case where the bidder j does not exist Denote the optimal spectrum allocation if the bidder j does

not exist as M* Then the minimum winning price charged to bidder j can

be given by

If xj > aj, bidder j’s request is granted If xj < aj, bidder j’s request is not granted If xj = aj, bidder is indifferent between winning and losing

Next, we consider the first or second price auction

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Auction design for multiple unit grant (cont’d)

The expected payoff obtained by jth bidder is given by

Consider the cases if xj ≠ rj and find that no case is betterOptions Cases Win? Expected payoff

xj < rj

rj > xj > aj O (rj – aj)

rj > aj > xj X 0aj > rj > xj X 0

xj > rj

xj > rj > aj O (rj – aj)

xj > aj > rj O (rj – aj) < 0 (*)

aj > xj > rj X 0

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Auction design for multiple unit grant (cont’d)

The expected payoff is

To keep Ej > 0, xj < rj. To remain winning, xj > aj. Thus dominant strategy is rj > xj > aj. Thus the reservation price is the upper bound

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Simulation model and results Results for single unit grant

Substitutable spectrum bands The reservation price for each bidder is assumed to

follow Uniform(250, 300) The bids are assume to follow Uniform(100, 300) Fig. 4a and b:

We compare the auctioneer’s revenue for both sequential and concurrent

Observation: The revenue in the sequential auction is greater. With increase in number of bands and bidders, revenue in

sequential setting is almost 200% more than that in concurrent setting

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Simulation model and results (cont’d) Fig. 5a,b,c

We present the revenue with increase I DSA periods Observation:

The difference between sequential and concurrent increases With increasing number of bands, sequential auction reaches

steady state much faster. Thus sequential auction is a better choice for auctioneer.

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Simulation model and results (cont’d) Fig. 6a, b:

We present the optimal bid for a specific bidder to win a spectrum band

Observation: The optimal bid for current is less and even decreasing with m -

> n

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Simulation model and results (cont’d) Non-substitutable spectrum bands

The band’s true value follows Uniform(450, 500) Fig. 7a and b:

We present the revenue of auctioneer Observation:

Sequential auction provides better revenue

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Simulation model and results (cont’d) Fig. 8a, b, and c

We present the revenue with increase in auction rounds Observation:

The difference between sequential and concurrent setting is even more than that of the substitutable bands of previous case

Thus sequential auction is a better choice for auctioneer for both types of bands.

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Simulation model and results (cont’d) Results for multiple unit grant

We follow second price sealed-bid mechanism because it has more properties than first price mechanism

Auctioneer tries to maximize the revenue Then, we compare the synchronous and

asynchronous auction Simulation parameters

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Simulation model and results (cont’d) Fig. 9 and 10 compare revenue and spectrum

usage with increase in auction round. Observation:

Both revenue and usage are low at the beginning and subsequently increases with rounds

Synchronous auction is more steady and performs better

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Simulation model and results (cont’d) Fig. 11 and 12 show the average revenue and

usage with varying number of bidders for both the auction strategies Observations

Synchronous generates approximately 10% more revenue Synchronous reaches steady state faster The usage of synchronous is more.

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Simulation model and results (cont’d) Fig, 13 and 14 show the average revenue and

usage with increase in capacity in CAB Observation

With increase in CAB, synchronous provides more revenue and makes optimal use of CAB

And thus provides more incentive for the spectrum owner

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Simulation model and results (cont’d) Fig. 15 shows the probability of winning with

increasing number of bidders Observation

Synchronous auction has a significantly higher probability of winning.

This implies that bidders will be encouraged to take part in the synchronous auction

Thus increasing the competition among the providers and increasing the chance to generate more revenue

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Conclusion In this research, we investigate possible

auction mechanism for dynamic spectrum allocation. We first investigate single unit grant

Through analysis and simulation we show that The popular conception of concurrent auction does not

prove beneficial. And then multiple unit grant

Through simulation we show that It is in the best interest of both bidders and spectrum owner

to adopt the synchronous auction

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Comments This paper somewhat complement the reason

why authors adopt the auction proposed in their later work in ToN 2009.

However, in the beginning they remind us the FCC’s concern is not only maximizing spectrum owners revenue but also considering the fairness issue. But they in fact didn’t touch such issue. Instead, they argue another issue to let bidder

have incentive to participate in the auction. The incompleteness makes downgrades the

fluency of this paper.