Bidding into the Red: A Model of Post‐Auction Bankruptcy

• Date: 01 December 2007
• Author: SIMON BOARD
• DOI: http://doi.org/10.1111/j.1540-6261.2007.01290.x
• Published date: 01 December 2007

THE JOURNAL OF FINANCE •VOL. LXII, NO. 6 •DECEMBER 2007

Bidding into the Red: A Model of Post-Auction

Bankruptcy

SIMON BOARD∗

ABSTRACT

This paper investigates auctions where bidders have limited liability.First, we analyze

bidding behavior under different auction formats, showing that the second-price auc-

tion induces higher prices, higher bankruptcy rates, and lower utilities than the first-

price auction. Second, we show that the cost of bankruptcy critically affects the seller’s

preference over the choice of auction. If bankruptcy is very costly,the seller prefers the

first-price auction over the second-price auction. Alternatively,if the bankrupt assets

are resold among the losers of the initial auction, the seller prefers the second-price

auction.

AUCTIONS ARE BECOMING AN EVER MORE POPULAR way to allocate important, large-

scale property rights. A major concern in such large auctions is that agents may

bid aggressively, anticipating that they can declare bankruptcy if the good is

worth less than expected. This problem is frequently encountered when selling

large assets. For example, ITV Digital went bankrupt after aggressively bid-

ding for the right to broadcast Football League games, owing £178m.Default

is also common in procurement auctions. For example, Connex’s rail franchise

for southeast England was taken over by the government after it demanded ex-

tra subsidies to continue operating. These examples illustrate the prevalence

of post-auction bankruptcy and provide a cautionary tale: As auction mecha-

nisms become an increasingly useful tool for both government and industry,the

possibility of default should be taken into account when designing the auction.

The basic structure of the paper follows the seminal work of Waehrer (1995),

Rhodes-Kropf and Viswanathan (2000), and Zheng (2001). The seller first auc-

tions a good among a number of bidders. After the auction, uncertainty is

revealed and the winning bidder decides whether to declare bankruptcy or pay

his bid.1

The contribution of this paper is twofold. First, we analyze the effect of differ-

ent auction formats on bidding behavior. We find that the second-price auction

(SPA) induces higher prices, higher bankruptcy rates, and lower utilities than

the first-price auction (FPA). This analysis is important because the choice of

∗Board is from the Department of Economics, University of Toronto. I am indebted to Alan

Beggs, Jeremy Bulow, and Paul Klemperer for their guidance, and to an anonymous referee whose

comments greatly improved the paper. I would also like to thank Pat Bajari, Eiichiro Kazumori,

Jon Levin, John McMillan, Rob McMillan, Meg Meyer,Paul Milgrom, Andreas Park, Jos´

e Quintero,

Margaret Stevens, and Bob Wilson.

1The auctioneer is female, while the bidders are male.

2695

2696 The Journal of Finance

auction format is the primary mechanism through which the seller can affect

revenue. Moreover, such a choice can have substantial effects: In some simple

numerical examples, we show that moving from the FPAto the SPA raises prices

by 20% but also increases the probability of bankruptcy by 5% (see Table II in

Section III).

Our second contribution is to examine the effect of bankruptcy costs on the

seller’s revenue. While previous studies focus on the case of costless bankruptcy,

we show that the seller’s view of bankruptcy and her preference over the auction

format depend critically on the post-bankruptcy recovery rate. The analysis

focuses on three scenarios.

(1) Under the large-recovery scenario, the seller inherits any bankrupt assets

with relatively little efficiency loss. A special case of the large-recovery sce-

nario is the full-recovery model, where bankruptcy is costless. For example,

when the British government took over Connex’s rail franchise, many of the

assets and employees stayed in place with little change in performance.2

(2) Under the small-recovery scenario, the seller inherits any bankrupt assets,

valuing them significantly less than the winning bidder. One can think

of the bankrupt firm being run by the seller, albeit less efficiently, or the

assets being used for another purpose altogether. For example, the ITV

Digital bankruptcy led to large welfare losses: Customers fled the digital

operator at a rate of 7% per month, hundreds of employees were laid off,

and many football teams were forced into administration.3

(3) Under the resale-recovery scenario, we endogenize the recovery rate by

assuming that any bankrupt assets are resold among the losing bidders

from the initial auction. For example, soon after the 1996 C-block spectrum

auction, the largest bidder, NextWave, declared bankruptcy. In response,

the FCC reclaimed and resold the licenses NextWave purchased in the

auction.4

Our revenue results can be summarized as follows. Under large recovery, the

seller prefers auctions with high prices and a high probability of bankruptcy,

such as the SPA. Conversely, under small recovery, the seller prefers auctions

with a low probability of bankruptcy, such as the FPA. Under resale recov-

ery, the seller’s preferences are more subtle: She prefers auctions with low

bankruptcy rates ceteris paribus, but prefers the SPA over the FPA. Even

2See the Financial Times,“Connex’s£58m aid adds to rail fears”(12/12/02), and “Authority’s

patience finally reached the end of the line”(28/06/03).

3See the Financial Times,“Turmoil and ITV Digital owners throw in towel”(28/03/02), “ITV

Digital to cut 900 jobs as customers quit”(20/04/02), and “Football clubs slide deeper into cash

crisis after losing court battle over ITV Digital”(02/08/02).

4In fact, the FCC was so keen to reauction these licenses that they did so twice. The FCC initially

resold the licenses in 2001. The Supreme Court then decided this repossession contravened federal

bankruptcy law and ordered the FCC to return the spectrum. However,in 2005, the FCC received a

proportion of these licenses back in a settlement with NextWaveand reauctioned them successfully.

For background on this case, see Zheng (2001). Also, see WallStreet Journal,“NextWave Regains

Control of Wireless Licenses”(28/01/03), “NextWave–FCC Deal Frees Up Firm’s Idle Wireless

Spectrum”(21/04/04), and “FCC Begins Auction of Spectrum Licenses”(27/01/05).