Is the Optimal Auction a Beauty Contest? The Interaction of Market Allocation and Supervision

1. Is the Optimal Auction a Beauty Contest?The Interaction of Market Allocation and Supervision Matthew Bennett Université 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 (qL,qH) with probability of g and 1-g respectively. • Able to supply at competitive quantity where price = cost, or below (qi < qic).

9. Model Framework • Regulatory Authority; • Can audits firm with some probability b(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 FÎ(0,A). • Welfare: • Regulator maximises consumer welfare, net of firms cost and expected auditing cost from each firm; • Auction revenue not included.

10. Timing and Information • The regulator announces regulatory policy, b(b1,b2,q) , F(b1,b2,q)which by assumption iscompletely credible. • Nature picks two firms to compete in auction. • Firms bid in an sealed bid first price auction picking b given b(b1,b2,q) , F(b1,b2,q) . • Regulator announces both bid levels, Where tie, theregulator picks a tie-breaking rule and license is allocated. • Winning firm chooses level of q thatmaximises profit given b(b1,b2,q) , F(b1,b2,q)and b . • Audit is initiated depending on b(b1,b2,q) and firms are fined if qi < qic.

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. Bidding Stage Product Stage Competitive Partial Competitive Reveal Partial Competitive Non-Competitive Competitive Partial Competitive Non-Reveal 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.

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:

17. Reveal, Non-Competitive • LBI: • HP: • Auction constraint: • Choice of bi and b(.) • Increase bH to satisfy LBI • But this violates bidding rule • Optimal bL = bH = 0 • Result: Optimal auction is a beauty contest

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.

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 b(.)=0 • Both high participation and low incentive constraints are binding thus optimal bids are : • Welfare optimal when non-competitive equilibrium is optimal.

20. Numerical Solutions Non Revealing Equilibrium Revealing Equilibrium

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.

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.