Auctioning Capacity. R. Preston McAfee University of Texas. Auctioning Capacity, R. Preston McAfee, Page 1 of 20

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1 Auctonng Capacty By R. Preston McAfee Unversty of Texas Prepared for Australasan Econometrc Socety Meetngs July, 1998 Auctonng Capacty, R. Preston McAfee, Page 1 of 20

2 Overvew Mcrowave lnk market creaton Capacty auctoned by government Market desgn of nterest n ts own rght Other examples of capacty supply Bddng for capacty: Auctonng lcence to compete Shakeout model An experment Auctonng capacty to Cournot compettors Model of mcrowave competton and bddng Bdders are also after-market buyers Resale market most salent characterstc Outcome of Mexcan Mcrowave Aucton Auctonng Capacty, R. Preston McAfee, Page 2 of 20

3 Market for Mcrowave Connectons Mcrowaves are used for Hgh capacty phone lne lnks (buldng to buldng) Connectng moble phone towers to the system Lne of sght communcatons Telephone exchange connectons Satellte connectons (non-conflctng use) Two mcrowave transmtters Pont to pont mcrowave lnks. Crossed lnes are conflcts unless they occur at dfferent heghts. Auctonng Capacty, R. Preston McAfee, Page 3 of 20

4 A pont to multpont system. Elmnates conflcts by usng a central tower. (Hub and spoke system) Tradtonally lnks allocated by government admnstraton Problems Slow bureaucracy (2+ years n Mexco requred for approval) Complcated feasblty U.S. uses prvate companes to establsh feasblty Slght reconfguratons may have dramatc effects No mechansm for reconfgurng connectons Incentve to hold exstng lnk New technology: pont to multpont No prcng of (occasonally) scarce resource Mexcan legal requrement that spectrum be auctoned How to prce 1,000,000 unque goods? Shadow prces dffcult to estmate Auctonng Capacty, R. Preston McAfee, Page 4 of 20

5 Soluton: Create a compettve market for supply of mcrowave lnks Mcrowave lnks are an deal canddate for deregulaton No serous scale economes Suffcent spectrum avalable to endow many frms Many major users are natural spectrum admnstrators Market Desgn Goal n Mexco: Create a compettve market n supply of lnks Auctonng Capacty, R. Preston McAfee, Page 5 of 20

6 Mexcan Mcrowave Aucton Number of Lcenses Type Band Sze Coverage 15 Pont to Pont 23 GHz 56 MHz Natonal 10 Pont to Pont 23 GHz 100 MHz Natonal 10 Pont to Pont 15 GHz 56 MHz Natonal 5 per regon Pont to Multpont 10 GHz 60 MHz Regonal 2.7 GHz of rado spectrum 80 Lcenses Dfferent bands are mperfect substtutes Propagaton dstance Scatter (sze of cone) Volume of data transmsson per MHz Other substtutes Copper wre Fber optcs Satellte lnk Auctonng Capacty, R. Preston McAfee, Page 6 of 20

7 Other examples of capacty auctons PCS auctons Mneral rghts Outer contnental shelf ol Grazng rghts Satellte transponders Rado and TV spectrum (Australa and New Zealand) Arport landng rghts CO 2 polluton permts Import quotas (Australa, New Zealand and Columba) Auctonng Capacty, R. Preston McAfee, Page 7 of 20

8 Auctonng Capacty Two extremes: sellng the rght to partcpate, and sellng ncremental capacty Auctonng lcenses to compete Induces a tournament-lke structure, where frms bd for the rght to partcpate n a subsequent competton to sell to consumers. Types wll be used to denote dstnct characterstcs, such as margnal costs, fxed costs, qualty, wth hgher types beng better (lower cost, hgher qualty, etc.). Let profts, f frm has type t and other frms have types t - be ( t,t ). π Suppose m lcenses are sold at a prce equal to the bd of the m+1 st hghest bds. In an effcent equlbrum, the hghest m types wn the bddng. Let f m+1 be the densty of the m+1 st hghest type, gven a partcular frm's type. Auctonng Capacty, R. Preston McAfee, Page 8 of 20

9 Brthdate Tournament Qualfcaton: You must have dentfcaton (e.g. passport, drver s lcense) gvng the date of your brth n order to partcpate. Stage 1: Bddng to enter tournament The two hghest bdders wll gan entry nto a tournament. Each of these bdders wll pay the thrd-hghest bd. Stage 2: Tournament Take the month and day of the brthday (e.g. 15 Aprl s 415; 7 December s 1207). The entrant wth the hghest brthday wns $10, for a net earnng of $10 mnus the thrd-hghest bd. The other entrant loses the thrd-hghest bd and gans nothng. In the event of a te, each of the entrants gans $5, mnus the thrd-hghest bd. Auctonng Capacty, R. Preston McAfee, Page 9 of 20

10 Profts of a frm wth type t, f t bds B(r), are v(r,t ) r 0 ( E[ (t,t ) t s] B(s) ) fm+ 1(s t ) ds = π whch yelds B ( t) = E[ π ( t, t ) t t]. Ths canddate for equlbrum s an equlbrum f B s strctly ncreasng. It s straghtforward to show that the dscrmnatory aucton (pay your bd) has a canddate equlbrum B 1 (t) satsfyng: f ( t t) B 1( t) = [ B( t) B1( t)], F( t t) Thus, f B s nonncreasng around 0, so s B 1. In ths case, no effcent (selects the best types wth certanty) exsts. Auctonng Capacty, R. Preston McAfee, Page 10 of 20

11 Shakeout Aucton Suppose that the market can't support m frms, and that the lowest effcency frm wll be drven out of busness. Then E[ π( t, t ) t t] = 0. There s no effcent equlbrum (ether dscrmnatory or unform prce) for the shakeout aucton. Intuton for unform prce aucton: bd only matters f you te wth hghest excluded frm In ths event, gven entry, you are the worst entrant In shakeout aucton, ths guarantees elmnaton Would prefer to lose & not pay bd Bddng for lcenses wll create neffcent allocatons. Lke Brthday Tournament. Auctonng Capacty, R. Preston McAfee, Page 11 of 20

12 Analyss of mcrowave competton Standard models do a poor job, because here the spectrum buyers are also spectrum users. Cournot downstream competton has a surprsng property: bddng for capacty tends to symmetrze the ndustry, wth small frms gettng larger. Whle nterestng and applcable to such sales as electrcty generaton capacty and polluton permts, t s a poor model of mcrowave competton. Example: Lnear demand, costs capacty. q 2 2k, where k s frm 's In ths case, the aucton of a small amount of capacty results n the smallest frm buyng the capacty, unless the market s very close to monopoly orgnally. Auctonng Capacty, R. Preston McAfee, Page 12 of 20

13 Model: Suppose there are n frms, frm havng value of q mcrowaves of q q 2. 2β Let x be the capacty of frm, and p the market prce n the after market. Suppose as well that addtonal unts suppled to the after-market decrease p by at rate f. The assumpton that addtonal supply to the after-market decreases prce seems plausble, and provdes each frm wth "Cournot-lke" market power n the after-market. The model s unsatsfyng n that t has a conjectural varatons feel to t. Frm maxmzes π = q q 2 2β + p( x q ). Ths gves a frst order condton: dπ q 0 = = 1 p + φ( x dq β q ). Auctonng Capacty, R. Preston McAfee, Page 13 of 20

14 In addton, p s determned by n = 1 0. ( x q ) = Straght-forward manpulatons yeld: 1 p = n = 1 n = 1 x 1+ βφ β 1+ β φ and q = β( 1 p + φx 1+ β φ ). Ths ad hoc model has the followng propertes. It matters who holds the capacty. Prce decreases as capacty rses. Net buyers restrct purchases to drve down prce. Net supplers restrct sales to drve up prce. For f=0, the after-market s effcent. As fæ, after-market vanshes. The after-market s equvalent to an ceberg-type transactons costs model, where frms are prce-takers and π 2 q = q + p( x ) ( 2 q φ x β Bddng s qualtatvely smlar. q ) 2. Auctonng Capacty, R. Preston McAfee, Page 14 of 20

15 Consder the smultaneous ascendng aucton for nfntesmal unts. Frm s wllng to bd, f k s the next hghest: b dπ = dx dπ dx k = p+ ( x Effect of changng x on prce depends on conjectures about alternatve purchasers. Snce the game s one of full nformaton, we look for a bd b wth the property that x > 0 mples b = b, x = 0 mples b b. If all the after-market buyers are present n the aucton, the equlbrum wll be unque, wth each frm purchasng ts own demand, and no resale. (True n both cournot and ceberg type models.) Ths outcome s effcent. 2 β φ q ) 1+ βφ dp β φ + 1+ dx 1+ βφ Thus, the aucton tends to undo the neffcences of resale, rather than resale makng the aucton more effcent, as s usually alleged (but s not, n general, true, as Ausubel and Cramton demonstrate). Auctonng Capacty, R. Preston McAfee, Page 15 of 20

16 Some demanders not present n aucton When some frms that are not present n the aucton wll demand capacty, there wll be net postve supply by bdders to the after-market. In ths case, all of the buyers wll be net sellers n the resale market. There s no equlbrum n whch a sngle bdder corners the market. Auctonng Capacty, R. Preston McAfee, Page 16 of 20

17 Bds Compared to After-market Prces If f s near zero (after-market nearly effcent), the bd prce wll exceed the after-market prce, wth net sellers losng money on these sales. The losses arse because bg demanders are wllng to pay a premum to prevent small demanders from buyng spectrum and then resellng wth the consequent reducton n resale prce. In ceberg model, bd prce s always less than after-market prces, because ncentve to ncrease after-market prce s swamped by the transactons cost. Bd prce less than after-market prce was consstently observed n Australan and New Zealand mport quota auctons. Entry by non-users would tend to arbtrage away such dfferences. When bd prce exceeds after-market prce, however, arbtrage s not feasble. Auctonng Capacty, R. Preston McAfee, Page 17 of 20

18 Predctons about Who Buys In the cournot type model, the largest demanders wll be the largest supplers when the resdual demand (not represented n the aucton) s concentrated, and n partcular, when there s a sngle resdual demander. Wth a large, dspersed demand, the largest demanders wll be smaller resdual supplers. Effect of Spectrum Caps Spectrum caps ncrease the gans from trade only when the resdual market s large and concentrated. Bndng spectrum caps reduce bd prces. Auctonng Capacty, R. Preston McAfee, Page 18 of 20

19 Outcomes n Mexcan Mcrowave Market: Company 23 GHz 15 GHz Regons Alestra Three Amartel Three Bestel 156 Four BNMexco Three Constel 56 Dpsa Iusacell M_Cable 112 Marcatel 56 Mdtel 100 Fve TCA 56 One Telnor All Nne Telmex All Nne Untel 56 Telnor assembled nne regons on the same frequency Telmex assembled nne regons, all but one on the same frequency. The results of the aucton ndcate that spectrum caps were not bndng. Whether a sngle bdder would have cornered the market n the absence of spectrum caps s unclear. Nevertheless, the results corroborate models n whch auctons do not lead to excessve concentraton. Auctonng Capacty, R. Preston McAfee, Page 19 of 20

20 Conclusons Auctons of the rght to compete may not effcently select partcpants. The all-pay aucton s theoretcally a soluton, although t has some undesrable poltcal propertes (payment wthout permt). Auctons may mprove the effcency of resale markets, by dstrbutng capacty to lower resale transactons costs. Fears of auctons leadng to excessve concentraton appear unfounded n many envronments. Progress on understandng auctons of capacty depends on modellng mperfect resale downstream competton Mcrowave market s a natural venue for free-market allocaton of spectrum admnstratve assgnment slow and cumbersome wthout prcng, assgnment neffcent market wll permt adapton to changng crcumstances no major scale economes suffcent spectrum for competton rase substantal revenue Auctonng Capacty, R. Preston McAfee, Page 20 of 20