A Theory of Costly Sequential Bidding

December 12, 2018

The lead article in Volume 22, Issue 5 of the Review of Finance is A Theory of Costly Sequential Bidding by Kent Daniel and David Hirshleifer.  This paper explains why, in many real-life auctions such as M&A, bidders may engage in “jump-bids” – bid much more than needed to stay in the auction – when it might seem more prudent to bid the minimum possible increment

How to Bid in an Auction?

Auctions are important in many areas of business.  The most obvious is M&A, where multiple potential bidders compete to take over a target, but another is competing to hire away a star employee.  The bidder’s challenge is to win the auction without having to bid so much that he actually pays more than the target is worth to him.  This problem of a “winner’s curse” is serious, and may explain why many M&A deals destroy value for bidders.  For example, over just four years – between 1998 and 2001 – US firms destroyed $240 billion of shareholder value through M&A.  In a hiring setting, there are numerous examples of sports teams competing to hire a star player, and the winning team actually ends up overpaying.

Auctions also occur where the bidder is selling its own services rather than buying a target.  Outsourcing companies compete to win a contract and may end up bidding so low that it makes a loss.  For example, the collapse of the UK outsourcing company Carillion, and the current troubles of Capita and Interserve, stemmed in part from winning business that turned out to be unprofitable.

So it’s important to get the bid strategy right.  And it seems that the right strategy is actually a very simple one – bid the lowest amount that you need to, and quit the auction when the bid exceeds your value.  For example, let’s say there’s a painting that you value at $5,000. The minimum bid is $1,000, and the minimum increment is $100.  When the auction starts, you’ll bid $1,000.  If someone else bids $1,100, you then counter with $1,200.  There’s no gain to bidding any higher than that (say $2,000).  There’s a chance that your rival values the painting at less than $2,000, in which case bidding $2,000 leads to you paying more than you need to.  And if she values it at more than $2,000, jumping to $2,000 won’t lead her to dropping out.  If someone counters your $1,200 with $1,300, you increase to $1,400.  This continues until either everyone else drops out (in which case you buy the painting for less than your value of $5,000), or the price exceeds $5,000 (in which case you drop out).

The above strategy seems so obviously the right one that auction houses assume that bidders will follow it.  That’s why the auctioneer doesn’t actually invite bids.  Instead, he starts the bidding at $1,000 and increases it by $100 each time.  Bidders simply raise their hand if they want to stay in rather than calling out an actual bid, as there’s no point in bidding more than the minimum.

Costly Bidding

If all auctions followed the auction-house format, we’d see (a) a very large number of bids, as it takes a while before everyone else drops out, and (b) each bid only beating the last one by a small increment.  But it’s easy to see that many real-life auctions don’t follow this format.  In the recent takeover battle for Sky, the bid increments were several billion pounds.  In December 2016, Fox bid £18.5 billion for Sky.  The deal was held up for over a year because it was referred to the UK competition authorities.  By the time the UK government was ready to give the deal the green light, Comcast counter-bid £22.5 billion in April 2018.  Fox hit back with a £24.5 billion bid in July, and Comcast retaliated just hours later with £26 billion.  In the end, Comcast won the auction with a £30 billion bid in September 2018.

Why is reality so different from what the simple theory would predict?  Kent and David argue that this is because the simple theory makes a critical assumption – that bidding is costless.  In an auction house, it takes no effort to raise your hand.  So you don’t mind having to raise your hand several times before your rivals drop out.  There’s no need to force them to drop out faster with a jump bid, which might cause you to pay more than you need to – you just wear your rivals down in a war of attrition.

But in many real-life settings, bidding is costly.  For example, in an M&A setting, it takes substantial executive (and perhaps board) time to get a new bid approved, distracting them from their core business.  A bidder also needs to meet with and pay advisors, and may need to undertake regulatory filings and meet with shareholders to ascertain their support for a revised bid.  Indeed, actual wars of attrition are very costly in terms of numbers of lives lost.  Another type of cost is that there might be not actually be the opportunity to make a counter-bid.  For example, when bidding for an employee, if a rival firm makes a higher offer from you, the employee might simply accept the bid to resolve the uncertainty, rather than going back to you to see if you’ll counter.

Kent and David model the optimal auction strategy when bids are costly – and find that it is markedly different from the costless benchmark.  In particular, it is optimal to engage in jump bids.  In an M&A auction, there is no formal auctioneer who sets a minimum opening bid, but research shows that a relevant reference point is the highest price that the target reached recently.  So, if bidding were costless, a prudent opening bid might be just above that recent peak.  But in reality, opening bids are much higher – indeed, when Johnson and Johnson bought Neutrogena, it paid 70% over the price two weeks before the bid.

Why?  There are two advantages of a jump bid.  First, you might reduce your bidding costs.  By making a high bid right away, you save the costs of making several lower bids first.  Second, you might end up paying a lower price than you need to.  By making a jump bid (e.g. opening with $2,000), you signal that your valuation is high.  Thus, even if your rival values the asset at more than your opening bid (say $2,500), she might not bother counter-bidding because doing so is costly.  If she thinks that your valuation is high, she won’t win the auction anyway so there’s no point paying the bidding cost with little probability of success.  This is similar to how, in poker, raising the stakes by a large amount may cause others to drop out – staying in the game is costly as they’d need to put in money to do so.

Of course, there’s a cost to making a jump bid – you may up spending more than you need to.  So Kent and David conduct a formal analysis.  Curiously, they find that it may be optimal for the opening bidder to bid high enough to signal his entire valuation ($5,000 in the previous example) – and for the counter-bidder to bid her entire valuation minus the bid cost rather than just increasing the bid by $100.  Their theory has several implications for real-life auctions which differ from the standard model.  Many of them are consistent with casual empiricism, but many haven’t been formally tested and may be fruitful avenues for future research:

  • The auction will conclude with a small number of bids
  • Bids will occur with large jumps at each stage
  • In general, the higher the initial bid, the higher the jump to the second bid
  • Bidders will sometimes wait for long periods of time before entering an auction.

That last implication is particularly subtle.  If a bidder values the target at more than the minimum opening bid (e.g. the recent peak), he may still not choose to bid.  If his valuation only beats this minimum by a small amount, he’s worried that he’ll be beaten by a counter-bid, and so have wasted the cost of bidding.  But, if other potential bidders also don’t bid, he figures out that they can’t have high valuations either, and so becomes more confident and might eventually bid.  This is similar to poker where, in the opening round, a player with a mediocre hand may choose to “check” (pass but stay in the game) rather than pay the “ante” (minimum bid) – but may then pay the minimum bid if other players check, thus signalling that they don’t have strong hands either.

In reality, companies sometimes put themselves up for a takeover by announcing that they are “considering strategic options”, including a potential sale of the whole company.  Even without an active action from a company, the market may know it to be “in play” due to recent poor performance.  In those situations, it may take many months before someone chooses to bid, because it’s waiting to see what others might do.  Two interesting implications are that, the more time passes after a target becomes in play, the lower the target’s stock price drops (as delay signals that potential bidders don’t value it highly) and the lower any eventual opening bid.