ContrAuction: An Integrated Contract and Auction Design for Dynamic Spectrum Sharing

Transcription

1 ContrAuction: An Integrated Contract and Auction Design for Dynamic Spectrum Sharing Lin Gao Network Communications and Economics Lab (NCEL) Information Engineering Department The Chinese University of Hong Kong Joint work with Jianwei Huang, Ying-Ju Chen and Biying Shou Lin Gao (NCEL) ContrAuction 1 / 25

2 RADIO SERVICES COLOR LEGEND INTER- RADIO ASTRONOMY RADIODETERMINATION LAND LAND RADIO RADIO METEOROLOGICAL SPACE OPERATION AIDS EXPLORATION METEOROLOGICAL SPACE RESEARCH STANDARD FREQUENCY AND TIME SIGNAL STANDARD FREQUENCY AND TIME SIGNAL ACTIVITY CODE GOVERNMENT EXCLUSIVE GOVERNMENT/ NON-GOVERNMENT SHARED NON-GOVERNMENT EXCLUSIVE AL USAGE DESIGNATION SERVICE EXAMPLE DESCRIPTION Primary Capital Letters Secondary Mobile 1st Capital with lower case letters This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by the FCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changes made to the Table of Frequency Allocations. Therefore, for complete information, users should consult the Table to determine the current status of U.S. allocations. U.S. DEPARTMENT OF COMMERCE DMINISTRATION ANATIONAL TELECOMMUNICATIONS & INFORMATION U.S. DEPARTMENT OF COMMERCE National Telecommunications and Information Administration Office of Spectrum Management October (R) (RADIO BEACONS) (OR) 3 MHz LAND (OR) 5.73 * 5.90 * Mobile Mobile Fixed Aeronautical Mobile NOT ALLOCATED 3 khz 300 khz Aeronautical Radionavigation Aeronautical (Radio Beacons) (RADIO BEACONS) Radionavigation LAND LAND (AM RADIO) (R) Mobile* 23.2 (OR) ** STANDARD FREQ. AND TIME SIGNAL (25,000 khz) STANDARD FREQ. Space Research LAND LAND ** RADIO ASTRONOMY LAND ** ** ** LAND LAND ISM 6.78 ±.015 MHz ISM ±.007 MHz ISM ±.163 MHz 30 MHz 30 MHz ISM ±.02 MHz 300 MHz 300 MHz 3 GHz 30 GHz * Aeronautical Mobile (RADIO BEACONS) 335 Maritime Radionavigation (Radio Beacons) ** LAND (R) LAND Aeronautical Mobile RADIO ASTRONOMY Aeronautical Mobile (DISTRESS AND CALLING) (RADIO BEACONS) (RADIO BEACONS) (SHIPS ONLY) ASTRONOMY TRAVELERS INFORMATION STATIONS (G) AT 1610 khz 300 khz 3 MHz LAND 33.0 * (R) (OR) * STANDARD FREQ. AND TIME SIGNAL (5000 KHZ) STANDARD FREQ. Space Research ** (OR) Mobile (OR) STANDARD FREQ. AND TIME SIGNAL (10,000 khz) STANDARD FREQ. Space Research (R) Mobile* (OR) (R) (OR) (R) RADIO ASTRONOMY Mobile* Mobile* Mobile* STANDARD FREQ. AND TIME SIGNAL (15,000 khz) STANDARD FREQ. Space Research (OR) (R) (OR) Mobile STAND. FREQ. & TIME SIG. Space Research STANDARD FREQUENCY & TIME SIGNAL (20,000 KHZ) STANDARD FREQ. Space Research Mobile (DISTRESS AND CALLING) (TELEPHONY) STANDARD FREQ. AND TIME SIGNAL (2500kHz) STANDARD FREQ. Space Research STANDARD FREQ. AND TIME SIGNAL Maritime Radionavigation (Radio Beacons) Aeronautical Mobile Aeronautical Radionavigation (Radio Beacons) (R) (RADIO BEACONS) 3 GHz 300 GHz Background UNITED STATES FREQUENCY ALS THE RADIO SPECTRUM (R) (R) (R) LAND Radio Astronomy LAND LAND LAND (TV CHANNELS 2-4) (TV CHANNELS 5-6) (FM RADIO) 3.4 (R) (R) (TV CHANNELS 7-13) (R) (R) 34.0 Amateur (Ground) AERO. NAV.(Ground) SAT. (S-E) ** SAT. (S-E) (S-E) LAND Meteorological Satellite (S-E) (TV CHANNELS 14-20) LAND (TV CHANNELS 21-36) RADIO ASTRONOMY TV ** 4.99 RADIO ASTRONOMY Space Research AERO. RADIONAV. SAT (S-E) 5.25 RADIO 5.35 RADIONAV METEOROLOGICAL AIDS 5.65 RADIO Amateur 5.83 Amateur- sat (s-e) Amateur 5.85 SAT Amateur (S-E) Standard Frequency and Time Signal Satellite (S-E) Stand. Frequency 31.0 and Time Signal Satellite (S-E) 31.3 RADIO SPACE ASTRONOMY RESEARCH EXPLORATION SAT. SPACE 31.8 RESEARCH (deep space) 32.0 SPACE RES. INTER- SAT 32.3 INTER RADIO 36.0 SPACE RE. EXPL.. SAT SPACE RESEARCH (space-to-earth) 37.6 SPACE RES. (S-E) 38.0 SAT. (S-E) SAT SAT SAT. SPACE Earth RES. Sat Expl. (s - e) SAT EXPL 40.5 BCST BROAD- Fixed Mobile SAT. CASTING FX-SAT (S-E) 41.0 BROAD- BCST CASTING SAT RADIO ** ASTRONOMY RADIONAV. SAT RADIONAV.SAT. MOB. SAT FX SAT 48.2 FX SAT 50.2 SPACE RESEARCH EXPLORATION 50.4 FI XED SPACE EXPLORATION RESEARCH SPACE RES. INTER- SAT EXPL-SAT INTER- SAT SPACE RES. -ES 56.9 SPACE RES. -ES INTER- SAT 57.0 SPACE INTER EXPLORATION RES. - SAT SAT SPACE RESEARCH EXPLORATION SAT EXPLORATION SPACE INTER- LOC. SAT. RES.. SAT 59.3 * EXCEPT AERO (R) ** EXCEPT AERO WAVELENGTH BAND DESIGNATIONS ACTIVITIES (S-E) ISM 5.8 ±.075 GHz INTER ISM ±.250 GHz GHz IS DESIGNATED FOR UNLICENSED DEVICES 65.0 SPACE RESEARCH INTER- ** EXPLORATION SAT SPACE RESEARCH (S-E) (S-E) Fixed 7.30 (S-E) Mobile Satellite (S-E) 7.45 MET. Mobile (S-E) (S-E) Satellite (S-E) 7.55 Mobile (S-E) Satellite (S-E) Fixed EXPL. Mobile (S-E) Satellite EXPL. MET. Mobile SAT. (S-E) Satellite (no airborne) EXPL. Mobile Satellite (S-E) (no airborne) 8.4 SPACE RESEARCH (S-E) (deep space only) 8.45 SPACE RESEARCH (S-E) 8.5 RADIO Meteorological Aids RADIO INTER- NAVIGATION NAVIGATION BROADCAST 746 BROADCAST BROADCAST LAND 821 LAND 824 LAND LAND 866 LAND 869 LAND LAND RADIO Amateur LAND LAND LAND 940 LAND RADIOLOC. Amateur 77.0 RADIOLOC. Amateur Amateur Sat RADIOLOC. SAT 78.0 Amateur Amateur Satellite 81.0 (S-E) (S-E) 84.0 BROAD- BROAD- CASTING CASTING ISM ± 13 MHz EXPLORATION SPACE RESEARCH RADIO ASTRONOMY RADIO 10.0 Amateur Amateur Amateur Satellite 10.5 RADIO SPACE RESEARCH EXPL. RADIO SAT. ASTRONOMY RADIO SPACE EXPL. ASTRONOMY RESEARCH NAVIGATION NAVIGATION SPACE RESEARCH EXPL. (S-E) (S-E) EXPLORATION SPACE RESEARCH RADIO ASTRONOMY (S-E) Mobile ** ISM ±.500 GHz (Deep Space) RADIONAV. Space Research SPACE RESEARCH (S-E) (R) MOB. SAT. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) Mob. Sat. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) MOB. SAT. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) Mob. Sat. (S-E) SPACE RES. (S-E) SPACE OPN. (S-E) MET. SAT. (S-E) RADIONAV- LAND LAND LAND INTER SAT. Land Mobile SAT. Satellite Space Research RADIO NAVIGATION NAVIGATION NAVIGATION 14.2 Land Mobile Mobile** Satellite Land Mobile 14.4 Fixed Mobile SAT. Satellite Fixed Mobile FX SAT. L M Sat 14.5 Mobile Space Research Fixed Space Research Mobile Space Research RADIO ASTRONOMY SPACE RESEARCH EXPL. SAT AERO RADIONAV SAT RADIO 16.6 RADIO Space Res.(act.) 17.1 RADIO 17.2 Earth Expl Sat Space Res. RADIOLOC. Radioloc BCST SAT. FX SAT (S-E) 18.3 (S-E) 18.6 SPACE RES. FX SAT (S-E) EXPL. SAT (S-E) 19.3 (S-E) 19.7 (S-E) SAT. (S-E) 20.1 FX SAT (S-E) (S-E) 20.2 STD FREQ. & TIME FX SAT (S-E) SAT (S-E) 21.2 SPACE RES. EXPL. SAT ** SPACE RAD.AST ** EXPL. SAT. RES Amateur Amateur Satellite (S-E) EXPL. SAT. SPACE RES. (S-E) (S-E) LAND LAND LAND LAND Land Mobile Fixed MET. SAT. (s-e) EXPLORATION RADIO SPACE RES. ASTRONOMY INTER SPACE RESEARCH INTER- EXPLORATION SAT INTER RADIO SPACE RESEARCH ASTRONOMY EXPLORATION INTER NAVIGATION EXPLORATION SAT SPACE RES RADIO (TELEPHONY) LAND (TELEPHONY) Amateur Fixed Mobile LAND STD. FREQ. & TIME SIGNAL SAT. (400.1 MHz) MET. AIDS. SPACE RES. Space Opn. MET. SAT. (Radiosonde) SAT. (S-E) (S-E) (S-E) (S-E) MET. AIDS Earth Expl. (Radiosonde) (S-E) SPACE OPN. MET-SAT. EXPL Met-Satellite Earth Expl Sat SAT. Satellite MET. AIDS MET-SAT. EXPL Met-Satellite Earth Expl Sat (Radiosonde) SAT METEOROLOGICAL AIDS (RADIOSONDE) RADIO ASTRONOMY SPACE RESEARCH (S-S) RADIO Amateur 1215 (S-E) RADIO 1240 RADIO Amateur RADIO 1390 ** -SAT 1392 ** 1395 LAND 1400 RADIO ASTRONOMY EXPL SAT SPA CE RESEARCH ( Passive) 1427 LAND Fixed (TLM) LAND (TLM) (TLM) SAT (S-E) (TLM) LAND (TLM) 1432 ** 1435 ( TELEMETERING) 1525 SAT. Mobile ** (Space to Earth) SAT. SAT. Mobile 1530 (Space to Earth) (Space to Earth) (Aero. TLM) 1535 (space to Earth) (S-E) 1544 (S-E) 1545 (R) (space to Earth) Mobile Satellite (S- E) (R) (space to Earth) (Space to Earth) (R) (space to Earth) 1559 RADIONAV. (Space to Earth) 1610 AERO. RADIO DET. SAT. SAT AERO. RADIONAV. RADIO DET. SAT. SAT. RADIO ASTRONOMY AERO. RADIONAV. RADIO DET. SAT. SAT. Mobile Sat. (S-E) RADIO ASTRONOMY SAT RADIO ASTRONOMY SPACE RESEARCH METEOROLOGICAL RADIO ASTRONOMY AIDS (RADIOSONDE) 1670 ** 1675 METEOROLOGICAL METEOROLOGICAL (s-e) AIDS (Radiosonde) SPACE RES. EXPL. SPACE OP (s-s) SAT. (s-s) (s-s) MOB. FX S) (S-E) 2200 SPACE SPACE (LOS) RESEARCH OPERATION (LOS) EXPLORATION (s-e)(s-s) (s-e)(s-s) SAT. (s-e)(s-s) 2290 SPACE RES..(S-E) ** 2300 Amateur 2305 Amateur RADIO ** 2310 Mobile Fixed MOB FX R- LOC. B-SAT 2320 Mobile 2345 Fixed BCST- Mobile Fixed MOB FX R- LOC. B-SAT INTER- SPACE RESEARCH EXPL SAT MO- INTER- SPACE E A R T H Amatuer BILE SAT. RES. EXPL. SAT INTER- SPACE RESEARCH EXPL SAT INTER RADIO ASTRONOMY SPACE RES. EXPL. SAT EXPLORATION SPACE RESEARCH RADIO ASTRONOMY RADIO Fixed ISM ± 50 MHz NAVIGATION (S-E) SPACE RES. EXPL. (S-E) SAT (S-E) Amateur Satellite Amateur EXPLORATION SPACE RES METEOROLOGICAL AIDS INTER Earth INTER- Expl. Satellite (Active) RADIO RADIO INTER- Earth Standard Exploration Frequency and Satellite Time Signal (S-S) Satellite Earth std Exploration freq e-e-sat INTER-SAT. Satellite (S-S) 25.5 & time e-e-sat (s-s) INTER-SAT Earth Exploration INTER- Satellite (S-S) 27.5 SAT ISM ± GHz ISM ± 1GHz NAVIGATION NAVIGATION PLEASE NOTE: THE SPACING ALLOTTED THE SERVICES IN THE SPEC- TRUM SEGMENTS SHOWN IS NOT PROPORTIONAL TO THE ACTUAL AMOUNT OF SPECTRUM OCCUPIED RADIODETERMINATION SAT. (S-E) (S-E) 2500 BCST - SAT. ** FX-SAT (S - E) 2655 E-Expl Sat Radio Ast Space res. MOB** B- SAT. FX FX-SAT 2690 RADIO ASTRON. SPACE RESEARCH EXPL SAT GHz RADIO ASTRONOMY LAND LAND LAND LAND LAND LAND LAND LAND LAND STANDARD FREQ. AND TIME SIGNAL (20 khz) 3 x 10 7 m 3 x 10 6 m 3 x 10 5 m 30,000 m 3,000 m 300 m 30 m 3 m 30 cm 3 cm 0.3 cm 0.03 cm 3 x 10 5 Å 3 x 10 4 Å 3 x 10 3 Å 3 x 10 2 Å 3 x 10Å 3Å 3 x 10-1 Å 3 x 10-2 Å 3 x 10-3 Å 3 x 10-4 Å 3 x 10-5 Å 3 x 10-6 Å 3 x 10-7 Å VERY LOW FREQUENCY (VLF) LAND LF MF HF VHF UHF SHF EHF INFRARED VISIBLE ULTRAVIOLET X-RAY GAMMA-RAY COSMIC-RAY Audible Range AM Broadcast FM Broadcast P L S C X Radar Bands Radar Sub-Millimeter Visible Ultraviolet Gamma-ray Cosmic-ray Infra-sonics Sonics Ultra-sonics Microwaves Infrared FREQUENCY 0 10 Hz 100 Hz 1 khz 10 khz 100 khz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1 THz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz INTER- ** THE RADIO SPECTRUM 3 khz MAGNIFIED ABOVE 300 GHz X-ray Standard Freq. and STANDARD FREQ. AND TIME SIGNAL (60 khz) Time Signal Satellite Space Research Amateur Earth Expl. Satellite (Active) Amateur Frequency allocation (USA): Over-crowed Spectrum utilization (Berkeley): Inefficient Dynamic Spectrum Access Goal: Increase spectrum efficiency and alleviate spectrum scarcity Basic idea: Allowing unlicensed users to access licensed spectrum Requirement: Provide economic incentive for both primary spectrum owners and cognitive radio users Secondary Spectrum Market Lin Gao (NCEL) ContrAuction 2 / 25

3 Economics of dynamic spectrum access: spectrum trading Secondary Spectrum Market Government regulator Primary market Spectrum licensee (Spectrum owner) Secondary market Cognitive radio user Dynamic spectrum access Spectrum primary market Figure vs 11.1 secondary Government market regulator, [E. Hossain, spectrum D. Niyato, owner, Z. Han and cognitive 09] radio Secondary Spectrum Market Dynamic spectrum access Seller: Primary spectrum owner (PO) Buyer: Cognitive radio user (secondary user, SU) Item: Spectrums licensed to the PO Scheme: Short-term vs Long-term Spectrum trading - Spectrum sensing - Spectrum pricing - Cognitive MAC - Spectrum utility - Routing and higher - Competition and layer protocols cooperation e.g., in a slot-by-slot manner (millisecond or second scale) We focus on a monopoly secondary spectrum market (1 PO). Figure 11.2 Dynamic spectrum access and spectrum trading. Lin Gao (NCEL) ContrAuction 3 / 25

4 Hybrid Market Structure Hybrid Market Structure Spot Market Buyers compete openly for spectrums in a real-time and on-demand manner (e.g., through an auction) Flexibility: Allow SUs to compete for spectrums based on their real-time demands Burst traffic or Elastic services (e.g., file transferring) Future Market Buyers enter into certain aforehand agreement (called a contract, specifying the spectrum demand, price, etc.) with the seller Certainty: Insures SUs (PO) against future uncertainty in market supply (demand) Period traffic or Inelastic services (e.g., Netflix video streaming) Main advantage Flexible in achieving desirable QoS differentiations Lin Gao (NCEL) ContrAuction 4 / 25

5 Our Contribution Problem: PO s Profit Maximization How should a monopoly PO sell his spectrums among contract users and spot market users to maximize his overall profit? Novelty and main contribution New modeling and solution technique The first work tackling secondary spectrum trading with the coexistence of future and spot markets Multiple information scenarios Studying the optimal selling mechanisms under both information symmetry and asymmetry Lin Gao (NCEL) ContrAuction 5 / 25

6 The Network Model Network Model One primary spectrum owner (PO) Transmission protocol: Slotted (e.g., GSM, WCDMA, and LTE) Spectrum opportunity: Idle spectrum (unused by licensed holders) Sharing scheme: Short-term, i.e., in a slot-by-slot manner Multiple secondary users (SUs) Unlicensed: Eager for spectrums Valuation: Benefit from using some spectrums Service type: Elastic and Inelastic Spot and Future market Idle Spectrum Un-reservable Allocate in real-time Dynamic across time Not know future information Heterogeneous among users User valuation diversity Each spectrum can only be used by one SU at the same time (Spatial reuse is not considered in this work) Lin Gao (NCEL) ContrAuction 6 / 25

7 The Market Model Hybrid Spectrum Market Model One seller (PO) Monopoly market Trading scheme: Short-term, i.e., in a slot-by-slot manner S: Idle spectrums in a specific time period (say T slots) M: Spot purchasing buyers (SUs) in the spot market Compete openly for spectrums only when needed Price based on the real-time valuation and market competition v m: Valuation of spot market user m Maximal willingness-to-pay N : Contract buyers (SUs) in the future market Pre-defined spectrum demand, payment and penalty (in one period) C n {B n, D n, P n}: Contract signed by user n N u n: Valuation of contract user n Long-term satisfaction Lin Gao (NCEL) ContrAuction 7 / 25

8 The Network Information Network Information All SUs valuations for any idle spectrum Denoted by θ (v 1,..., v M, u 1,..., u N ) Random Vector Complete network information Not practical! The PO knows the information θ of every spectrum in advance Incomplete network information The PO does not know the precise information θ of every future spectrum, but only the stochastic distribution of θ, i.e., f (θ) Symmetric: The PO can observe the SUs realized valuations for the current spectrum (but not those for the future spectrums) Asymmetric: The PO cannot observe the SUs realized valuations for the current spectrum Information Symmetry/Asymmetry Spot Trading Mechanism Lin Gao (NCEL) ContrAuction 8 / 25

9 Jianwei TheHuang, Model Ying-Ju Chen, An and example Biying Shou roper economic incenspectrum sharing, and is one effective way to er secondary spectrum y spectrum owner, PO) sers, SUs) in a hybrid ontract buyers (future arket). We focus on the work information, and ization problem, where iding the allocation of Fig. 1. An illustration of the hybrid spectrum market. mation realization. We Example 1: hybrid spectrum market [L. Gao, J. Huang, etc. 12 ] nder both information sharing, where POs temporarily lease the un-utilized (idle) ending on whether the spectrums to unlicensed SUs to obtain additional profit. In this ion. Under information An example solution (benchmark) t (optimality) and the ation asymmetry, an sary for eliciting the the ContrAuction, an, where the PO acts ole of an auctioneer) e derive the optimal iency, and characterize that under information nt for the SUs. Spectrum (Channel) Future Market 4 t PO Busy Channel a b Spot Market Idle Channel Time (Slot) paper, we consider the short-term secondary spectrum trading (e.g., on a slot-by-slot basis) between a single PO (monopoly Seller s seller) supply: and multiple S = {c1,..., c SUs (buyers) 18 } in total T = 12 slots in a hybrid spectrum market Spot market: with both M the = future {a, market b, c, d} and the spot market. In the future Future market, market: each N SU = reaches {1, 2, 3, an 4} agreement, called a guaranteed Two idle contract, spectrums directly at with time the PO. T = The t contract are sold pre-specifies to contract some buyer 3 and key elements in trading, e.g., the price and the demand in a spot market buyer a, respectively. future period. In the spot market, the SUs compete openly with each other for spectrums (e.g., by an auction), and each spectrum is traded in a real-time and open manner. Figure Lin Gao (NCEL) ContrAuction 9 / 25 c d

10 Problem Description and Approach Vertical: spectrum exclusive-usage constraint How to sell the spectrum at each slot t?? t-1 t t+1 Horizontal: demand constraints of contract users T-1 T How to determine the allocation and charge for every spectrum in real-time under incomplete information? Time Approach Infinite-Dimensional Optimization Every information realization θ Allocation strategy A(θ) A(θ) ( a 0 (θ), a 1 (θ),..., a N (θ) ), θ Θ a 0(θ) [0, 1]: allocation probability to the spot market a n(θ) [0, 1]: allocation probability to the contract user n N Constraints User-coupling constraint: N n=0 an(θ) 1, θ Θ Time-coupling constraint: Dn an(θ)f (θ)dθ < Penalty, n N θ S Lin Gao (NCEL) ContrAuction 10 / 25

11 Problem Formulation Problem Formulation PO s Profit Maximization N N maximize E[R 0 ] + E[R n ] w n E[C n ], A(θ), θ n=1 n=1 subject to a n(θ) [0, 1], n {0, 1,..., N}, θ Θ; N n=0 an(θ) 1, θ Θ. E[R 0 ] S θ a 0(θ)r 0 (θ)f (θ)dθ: Expected profit from the spot market r 0(θ): PO s maximum profit as selling a spectrum θ on the spot market, depending on spot trading mechanism E[R n] B n [D n E[d n]] + Pn: Expected profit from the contract user n E[C n] S θ an(θ)cn(θ)f (θ)dθ: Expected cost from the contract user n w n: weight of contract user n s long-term satisfaction loss (cost) E[d n] S θ an(θ)f (θ)dθ: Expected number of spectrums to contract user n Lin Gao (NCEL) ContrAuction 11 / 25

12 Information Symmetry The PO can observe the SUs realized valuations at each time slot Optimal Pricing: Charging whatever the spot market will bear Spot Trading Mechanism Perfect Price Discrimination r 0 (θ) = YM 1 (θ) max v m m M Allocate each spectrum to the highest valuation user Charge the allocated user a price exactly same as its valuation Lin Gao (NCEL) ContrAuction 12 / 25

13 Equivalent Transform Condition I (Full Spectrum Utilization) N n=0 a n (θ) = 1 a0 (θ) = 1 N n=1 a n (θ) Condition II (No Contract Overflow) E[d n] S θ an(θ)f (θ)dθ Dn E[Rn] Bn (Dn E[dn]) P n Equivalent Optimization Problem N maximize F + S H n (θ)a n (θ)f (θ)dθ A 0 (θ), θ n=1 subject to (i) a n(θ) 0, n N, θ Θ θ (ii) (iii) N n=1 an(θ) 1, θ Θ E[d n ] D n, n N A 0 (θ) A(θ)/{a 0 (θ)} = ( a 1 (θ),..., a N (θ) ) : New allocation strategy H n(θ) r 0 (θ) + P n w nc n(θ) F S θ r 0(θ)f (θ)dθ + N ( n=1 Bn P ) nd n : Constant Lin Gao (NCEL) ContrAuction 13 / 25

14 Primal-Dual Method Dual Variables: µ n (θ), η(θ), λ n, n N Lagrangian: L n=1 θ L(θ)f (θ)dθ Sub-Lagrangian L(θ) N N L(θ) F + S H n (θ)a n (θ) + µ n (θ)a n (θ) + η(θ) ( 1 N a n (θ) ) + n=1 n=1 n=1 N ( λ n Dn S a n (θ) ) Lin Gao (NCEL) ContrAuction 14 / 25

15 First-order Derivative of L(θ) Marginal Profit L (n) (θ) L(θ) a n (θ) = S H n(θ) + µ n (θ) η(θ) S λ n Mantle Marginal Profit Core Marginal Profit J (n) 1 (θ) S H n (θ) η(θ) S λ n J (n) 2 (θ) S H n (θ) S λ n L (n) (θ): marginal profit, the first-order derivative of L(θ) with respect to a n(θ) J (n) 1 (θ) = L (n) (θ) µ n(θ): eliminate µ n(θ) from the marginal profit J (n) 2 (θ) = L (n) (θ) µ n(θ) + η(θ): eliminate µ n(θ) and η(θ) from the marginal profit Lin Gao (NCEL) ContrAuction 15 / 25

16 First-order Condition and Duality Principle Optimal Primary Solution an(θ) 0, L (n) (θ) < 0 an(θ) = 1, L (n) (θ) > 0 δ [0, 1], L (n) (θ) = 0 Dual Constraints µ n(θ) 0, an (θ) 0, µn(θ)a n (θ) = 0, n N, θ Θ η(θ) 0, 1 N n=1 a n (θ) 0, η(θ) ( 1 N n=1 a n (θ) ) = 0, θ Θ ( λ n 0, D n E[d n] 0, λ n Dn E[d ) n] = 0, n N Duality Principle Finding optimal primary solution Finding optimal dual variables satisfying dual constraints Lin Gao (NCEL) ContrAuction 16 / 25

17 Optimal Dual Variables µ n(θ), η (θ) Lemma 3 Optimal conditions for µ n(θ) J (n) 1 (θ) 0 µ n (θ) = 0 J (n) 1 (θ) < 0 µ (n) n (θ) [0, J 1 (θ) ] µ n (θ) never changes the sign of marginal profit: sign{l(n) (θ)} sign{j (n) 1 (θ)} Lemma 4 Optimal conditions for η (θ) { K1 (θ) 0 η (θ) [max(0, K 2 (θ)), K 1 (θ)] K 1 (θ) < 0 η (θ) = 0 K 1 (θ) max n N J (n) 2 (θ): the highest core marginal profit K 2 (θ) max n N /n1 J (n) 2 (θ): the second highest core marginal profit η (θ) reduces identically all marginal profits such that at most one is positive Lin Gao (NCEL) ContrAuction 17 / 25

18 Optimal Dual Variables λ n Lemma 6 Optimal conditions for λ n { } λ n = max 0, arg λn S f (θ)dθ = D n θ Θ + n (Λ n,λn) Θ + n { θ J (n) 2 (θ) > 0&J (n) 2 (θ) > max i n J (i) 2 (θ)} : spectrums to contract user n. λ n shifts vertically user n s marginal profit to meet demand constraint E[dn] Dn Optimal solution a n(θ) an(θ) = 1 J (n) 2 (θ) 0 & J (n) 2 (θ) max J (i) 2 (θ) i n Intuitively, allocate each spectrum with θ to the contract with highest and positive core marginal profit J (n) 2 (θ) Lin Gao (NCEL) ContrAuction 18 / 25

19 Solution Summary (Information Symmetry) Optimal Selling Mechanism Perfect Price Discrimination Price definition pm (θ) v m for spot market user m M pn (θ) P n w n c n (θ) λ n for contract user n N Allocation strategy Allocate each spectrum θ to the highest price user Charge scheme Charge user s price or valuation v m if a spot market user m wins Charge a pre-defined price if a contract user n wins Comments Contract user s price depends on penalty rather than payment; Shadow price λ n reduces contract user n s price to meet demand constraint; Lin Gao (NCEL) ContrAuction 19 / 25

20 Information Asymmetry The PO cannot observe the SUs realized valuations at each time slot Incentive compatible mechanism Truth-telling of spot market users Spot Trading Mechanism VCG-based Auction r 0 (θ) = YM 2 (θ) max v m m m Allocate each spectrum to the highest bid user Charge the allocated user a critical value (e.g., the second highest bid in a second-price auction) Lin Gao (NCEL) ContrAuction 20 / 25

21 Auction in Hybrid Market Challenge I How to involve contract users into the spot auction? Not willing to be involved in the competition of an auction Not able to be involved in the competition of an auction Solution ContrAuction The PO acts as virtual bidders on behalf of the contracts Mechanism is transparent to the contract users Challenge II How to determine the optimal bid for each contract? No external relevance: each contract user s bid is irrelevant to other users information ensure truthfulness of spot market users Efficiency constraint: achieve the same spectrum allocation as in information symmetry outcome is transparent to the contract users Lin Gao (NCEL) ContrAuction 21 / 25

22 ContrAuction and Optimal Bidding Rule Integrated Contract and Auction Design ContrAuction An VCG-based Auction as the underlying spot trading mechanism Basic idea: the PO acts as virtual bidders on behalf of the contracts Mechanism is truthful to the spot market users Mechanism and Outcome are transparent to the contract users Optimal Bidding Rule (under Efficiency Constraint) b n(θ) P n w n c n (θ) λ n bn (θ): contract user n s own information and a shadow price λ n given by Lemma 6 Efficiency: achieves the same allocation as in information symmetry Optimality: maximizes the PO s profit among all efficient mechanisms. Lin Gao (NCEL) ContrAuction 22 / 25

23 Solution Summary (Information Asymmetry) Optimal Selling Mechanism ContrAuction Bidding strategy bm (θ) v m for spot market user m M (truthfulness) bn (θ) P n w n c n (θ) λ n for contract user n N Allocation strategy Allocate each spectrum θ to the highest bid user Charge scheme Charge the second highest bid if a spot market user wins Charge a pre-defined price if a contract user wins Comments Contract user s bid is same as the price in information symmetry; Contract user s bid has exactly the same effect as a reserve price. Lin Gao (NCEL) ContrAuction 23 / 25

24 Conclusion and Future Work Conclusion Secondary spectrum trading with the coexistence of future and spot markets; PO s profit maximization under incomplete information; Optimal selling mechanisms under both information symmetry and asymmetry. Future Work Spatial Reuse: interference protocol model and physical model Without efficiency constraint: optimal ContrAuction mechanism Lin Gao (NCEL) ContrAuction 24 / 25

25 Contact Dr. Jianwei Huang ncel.ie.cuhk.edu.hk Lin Gao (NCEL) ContrAuction 25 / 25