Is the Optimal Auction a Beauty Contest?

The Interaction of Market Allocation and Supervision

Matthew BennettUniversité de Toulouse

(GREMAQ)

November 2003

2

Motivation

• Rise in popularity of licenses to create competition for the market.– Auctions for multiple licences in

competitive markets.

– Auctions for monopoly licence.

• Auctions for Monopoly licence– Infrastructure (Railtrack)

– Local Television licences UK

– Gas storage capacity

– Local loop access

3

Definitions

• Auction– A mechanism in which the highest bidding firm

wins the license.

– May also have some conditions on auction participation.

• Beauty Contest– A mechanism in which the license is sold for a

fixed monetary value (regardless of the firm type).

– Allocation of license is decided by the highest levels of service.

• Lottery– License is randomly allocated between

competing firms.

4

Why Auctions?

• Auctions as a selection tool:– The firm with the highest valuation will

be the most efficient firm and will win the license.

• Auctions have no impact:– Standard theory says bids are sunk

costs and thus have no impact.– Thus valuable source of tax revenue.

• Auction as additional regulatory tool– Suppose regulator wants to ensure

firms reveal cost types at auction stage– Regulator can allow firms to price

above competitive level in return for revealing types.

5

Main Results

• Auctions cannot bypass regulation

• The optimal auction is a beauty contest.

• Auctions/Beauty properly designed more efficient than a random allocation.

• Other mechanisms can increases welfare above auction/beauty contest.

• Maximising bid revenue is synonymous with high costs of capital countries.

6

Literature

• Little work on impact of licences on subsequent product market.– Bennett (2000)

• Uncertainty on type of regulator, model of susceptibility to lobbying.

– Jehiel and Moldavanu (2000)• Multiple licenses: Firms with greatest

tendency to collude in product market have highest valuations, thus auctions pick most collusive firms

– Klemperer (2001)• Summary of EU auctions and description of

what went wrong in ‘unsuccessful’ auctions.

7

Literature

• Asymmetrical information literature;– Baron and Myerson (1982)

• Regulatory contract literature.

– Besanko and Spulber (1989)• Anti trust authority using probability of

audit to ensure firms of different types do not collude.

• Do not consider impact of auction.

– Laffont and Tirole (1993)• Many asymmetric information regulatory

models.

• Most relevant to this paper is use of auctions to select a monopolist. Uses fixed transfers rather than audit technology.

8

Model Framework

• Two stage game;– 2 Firms bid for right to produce in

auction stage.

– Winning firm picks level of output (qi) Price is given by inverse demand function p(qi).

• Firms;– Firms picked from a population of two

marginal cost types (L, H) with probability of and 1- respectively.

– Able to supply at competitive quantity where price = cost, or below (qi < qi

c).

9

Model Framework

• Regulatory Authority;– Can audits firm with some probability

(b1,b2,q) chosen by the regulator.

– Auditing firm costs regulator K.

– If qi is less than competitive qic it is able

to impose a fine F where F

• Welfare:– Regulator maximises consumer

welfare, net of firms cost and expected auditing cost from each firm;

– Auction revenue not included.

KqbbqdqqpW iiiii

q

ii

i

),,( 20

10

Timing and Information• The regulator announces regulatory policy,

(b1,b2,q) , F(b1,b2,q) which by assumption is completely credible.

• Nature picks two firms to compete in auction.

• Firms bid in an sealed bid first price auction picking b given (b1,b2,q) , F(b1,b2,q) .

• Regulator announces both bid levels, Where tie, the regulator picks a tie-breaking rule and license is allocated.

• Winning firm chooses level of q that maximises profit given (b1,b2,q) , F(b1,b2,q) and b .

• Audit is initiated depending on (b1,b2,q) and firms are fined if qi < qi

c.

11

Equilibria

• Multiple possible outcomes;

• Simplification – Fully competitive market can be ruled out due

to cost of auditing.

– High cost firm pricing above cost whilst low firm prices at cost not compatible with firms’ incentives.

• Thus there are only 4 possible equilibria.

Reveal

Non-Reveal

Competitive

Partial Competitive

Partial Competitive

Non-Competitive

Bidding Stage Product Stage

Competitive

Partial Competitive

Partial Competitive

Non-Competitive

12

Firm Constraints

• Market Incentive Constraint:– Quantity chosen must be at least as

good as any other given bid strategy.

• Participation Constraint:– Firm must at least break even.

• Bidding Constraint:– Firm bid strategy must be as least as

profitable as any other bid strategy.

FqbbqFqbbq jiijiiii ),,(,),,(, 22

0),,(, 2 iiiii bFqbbq

iiii bUEbUE

13

Solution Methodology

• Game Solution Methodology– Solve for each of the sub-games in turn,

assuming optimal bidding strategy.

– Compare each of the sub-games to determine under which circumstances they are optimal.

• Sub Game Methodology– Determine which constraints bind.

– Solve for optimal audit policy

– Maximise welfare with respect to quantity taking account of binding constraints.

14

Non-Reveal Results

• Results in the Non-Reveal are same as those for a random allocation (Besanko & Spulber 1989).

– Full competition is pareto dominated• Second order advantage in higher quantities

outweighed by first order cost of audit.

– Full collusion may be optimal• As audit costs become sufficiently high

becomes more costly enforcing competition on high type.

15

Reveal Results

• Basic non-reveal results still hold.

• Auction cannot rule out necessity for costly audit.

• Optimal auction monetary bids are identical and hence the optimal auction is identical to a beauty contest.

• Welfare always higher with an auction/beauty contest compared to a random allocation.

16

Revealing Auction

• Regulator creates a policy such that it is optimal for firms to reveal their types within the auction stage.

• Incentive constraints, can combine to provide a joint constraint:

• PC;– As normal in these models if HP holds LP also

holds

• Welfare when efficient firm wins tie break:

•

2

1HL qq

KqqV

KqqVKqqVWE

HHHHH

LHLLLLLLLL

2

2

1

12)(

17

Reveal, Non-Competitive

• LBI:

• HP:

• Auction constraint:

• Choice of bi and (.)

– Increase bH to satisfy LBI

– But this violates bidding rule

– Optimal bL = bH = 0

• Result: Optimal auction is a beauty contest

HHHLH

LLHLLLLLLL

bFq

bFqbFq

,2

1

,1,2

0,2

1

HHHHH bFq

0 HL bb

18

Reveal, Non-Competitive

Optimal Quantities

• Result:– Even though a beauty contest is more

restrictive, it is equivalent to auction.

– Audit still required but at lower levels.

– Increased allocation efficiency.

– Auction/Beauty strictly increases welfare over a random allocation.

LL

L

LLLL

L

qq

qPqP

A

KqP

q

WE 1)(

LH

H

HHHH

H

qq

qPqP

A

KqP

q

WE 1)(

19

‘Service’ Auction• Beauty contest uses the best proposed service levels

to allocate licence, auctions uses highest bid, service auction combines both.

• Firms submit bids and service levels, regulator offers the license to a low service (high cost) firm at a high price or a high service (low cost) firm at a low price.

• Increases welfare because:– Enables regulatory authority to increase bH such that

the incentive constraints hold without having to award licence to high type.

– This is costless and allows (.)=0– Both high participation and low incentive constraints

are binding thus optimal bids are :

• Welfare optimal when non-competitive equilibrium is optimal.

HHH qb , 0Lb

20

Numerical SolutionsNon Revealing Equilibrium

Revealing Equilibrium

For values of µi such that qmL < qcH the comparison between equilibria isambiguous. In general as K increases relative to A the di®erence between thetwo equilibria come close to 0 until at large levels of K the optimal equilibriaswitches to the collusive equilibrium. Numerical solutions are best used toillustratethispoint. For easycomparisonweusethesameparameter evaluationsas Besanko and Spulber where P (q) = 100¡ qi , µH = 70, µL = 20, ° = 0:5,A = 2000and K as thevarying parameter.

Comparison of Welfare within Non-Revealing Bidding Strategy

Non Reveal, Partial Comp. Non Reveal, Full CollusiveK qL qcH ¯H ¼L W qL qH ¯H ¼L ¼H W0 80.0 30 0.75 0 1825 66.8 17.7 .109 882.9 0 174350 78.1 30 .676 148.8 1807 66.7 17.7 .109 885.8 0 1741100 76.4 30 .611 277.7 1791 66.7 17.8 .109 888.9 0 1738150 74.8 30 .555 390.2 1777 66.6 17.8 .108 892.1 0 1735180 73.9 30 .525 450.9 1769 66.6 17.9 .108 894.1 0 1733190 73.6 30 .514 470.1 1766 66.6 17.9 .108 894.7 0 1733200 73.3 30 .506 488.9 1763 66.5 17.9 .108 895.4 0 1732400 68.6 30 .358 783.7 1721 66.3 18.2 .107 910.3 0 1722600 65 30 .262 975 1690 65 15 0 975 225 1713

Table 1 shows the partially competitive and non-competitive equilibriumwithin a non-revealing equilibrium. With the sameoptimal solutions, thewel-fareresultsandhencetheconclusion is identical tothat of BesankoandSpulber,wherethecost of detectionK increasesthenon-competitiveequilibriumbecomesoptimal.

Full Reveal, Partial Comp. Full Reveal, Full Non-Comp. - bL >bHK qL qcH ¯H ¼L W qL qH ¯H ¼L ¼H W0 80 30 0.75 0 2512.5 74.2 25.8 0.05 429.5 0 2497.750 78.1 30 0.53 148.8 2504.6 74.0 26.2 0.05 437.3 0 2497.1100 76.4 30 0.33 277.7 2499.2 74.0 26.7 0.04 445.7 0 2496.5150 74.8 30 0.16 390.2 2496.1 73.8 27.3 0.04 454.9 0 2496.0180 73.9 30 0.07 450.9 2495.2 73.8 27.7 0.03 460.8 0 2495.7190 73.6 30 0.04 470.1 2495.1 73.6 27.7 0.02 470.1 27.7 2495.6200 73.3 30 0.02 488.9 2495.0 73.3 27.5 0 488.9 68.8 2495.1400 68.6 30 0 783.7 2463.5 68.6 23.3 0 783.7 155.6 2458.0600 65 30 0 975 2428.1 65 15 0 975 225 2400

Full Reveal, Full Non-Comp. - bL <bHN=A 61.1 7.7 0 1153.3 0 (171.5) 906.3

Optimal jNon-Auction Mechanism74.2 25.8 0 429.5 0 (109.0) 2497.7

5.0.3 Comparing Across Bidding Equilibria

Much more interesting is the comparisons across the bidding equilibria. Thiscomparison determineswhether or under what conditions theuseof an auction

23

For values of µi such that qmL < qcH the comparison between equilibria isambiguous. In general as K increases relative to A the di®erence between thetwo equilibria come close to 0 until at large levels of K the optimal equilibriaswitches to the collusive equilibrium. Numerical solutions are best used toillustratethispoint. For easycomparisonweusethesameparameter evaluationsas Besanko and Spulber where P (q) = 100¡ qi , µH = 70, µL = 20, ° = 0:5,A = 2000and K as thevarying parameter.

Comparison of Welfare within Non-Revealing Bidding Strategy

Non Reveal, Partial Comp. Non Reveal, Full CollusiveK qL qcH ¯H ¼L W qL qH ¯H ¼L ¼H W0 80.0 30 0.75 0 1825 66.8 17.7 .109 882.9 0 174350 78.1 30 .676 148.8 1807 66.7 17.7 .109 885.8 0 1741100 76.4 30 .611 277.7 1791 66.7 17.8 .109 888.9 0 1738150 74.8 30 .555 390.2 1777 66.6 17.8 .108 892.1 0 1735180 73.9 30 .525 450.9 1769 66.6 17.9 .108 894.1 0 1733190 73.6 30 .514 470.1 1766 66.6 17.9 .108 894.7 0 1733200 73.3 30 .506 488.9 1763 66.5 17.9 .108 895.4 0 1732400 68.6 30 .358 783.7 1721 66.3 18.2 .107 910.3 0 1722600 65 30 .262 975 1690 65 15 0 975 225 1713

Table 1 shows the partially competitive and non-competitive equilibriumwithin a non-revealing equilibrium. With the sameoptimal solutions, thewel-fareresultsandhencetheconclusion is identical tothat of BesankoandSpulber,wherethecost of detectionK increasesthenon-competitiveequilibriumbecomesoptimal.

Full Reveal, Partial Comp. Full Reveal, Full Non-Comp. - bL >bHK qL qcH ¯H ¼L W qL qH ¯H ¼L ¼H W0 80 30 0.75 0 2512.5 74.2 25.8 0.05 429.5 0 2497.750 78.1 30 0.53 148.8 2504.6 74.0 26.2 0.05 437.3 0 2497.1100 76.4 30 0.33 277.7 2499.2 74.0 26.7 0.04 445.7 0 2496.5150 74.8 30 0.16 390.2 2496.1 73.8 27.3 0.04 454.9 0 2496.0180 73.9 30 0.07 450.9 2495.2 73.8 27.7 0.03 460.8 0 2495.7190 73.6 30 0.04 470.1 2495.1 73.6 27.7 0.02 470.1 27.7 2495.6200 73.3 30 0.02 488.9 2495.0 73.3 27.5 0 488.9 68.8 2495.1400 68.6 30 0 783.7 2463.5 68.6 23.3 0 783.7 155.6 2458.0600 65 30 0 975 2428.1 65 15 0 975 225 2400

Full Reveal, Full Non-Comp. - bL <bHN=A 61.1 7.7 0 1153.3 0 (171.5) 906.3

Optimal jNon-Auction Mechanism74.2 25.8 0 429.5 0 (109.0) 2497.7

5.0.3 Comparing Across Bidding Equilibria

Much more interesting is the comparisons across the bidding equilibria. Thiscomparison determineswhether or under what conditions theuseof an auction

23

21

Bids in Welfare

• Addition of bid revenues.

– Alpha can be thought of as a cost of capital term.

• For low and medium levels of alpha:– The auction constraint still binds, thus

all previous main results hold.

• For high levels of alpha:– Desire for bid revenues means regulator

maximises low types profits, and thus auction constraint no longer binds.

iiiiii

q

ii bKqbbqdqqpWi ),,( 20

22

Conclusions

• Pure auctions restrict use of the bid as an instrument to determine firm types.

• Optimal policy under an auction is having both firms pay the same.– Thus the optimal auction is the same as a

beauty contest!

• Auctions/Beauty still increase welfare relative to a random license allocation

• Service Auction allows both the use of bid and audit probability whilst still allowing low type to win.– Increases welfare above level of auction within

non-competitive equilibrium.