The FT’s UK business editor has challenged me to solve a tricky problem for a misunderstood species: dragons. The dragons in question populate BBC2’s Dragons’ Den. Part of the fun of the show is watching these five ferocious venture capitalists give bungling inventors a roasting, but it’s equally entertaining to see them haggling over how large a share of a promising business the hopeful owners are willing to sell.
Merely by expressing an interest in a business, the dragons give the entrepreneurs confidence that they may be able to get a better offer elsewhere. Several recent hopefuls have decided that the dragons were too greedy and turned down their cash.
The first lesson for the rational dragon: curb your enthusiasm in public and make an offer in private. Although the rules of the show forbid it, perhaps some dragons already do. Their scornful put-downs could be motivated as much by rational calculation as by a mean streak or a mean TV producer.
The den is, in fact, an auction room by another name. Dragons bid against each other, and against the unknown outside offers that the business may receive, and they should be aware that every bid reveals information to the other dragons and the entrepreneur. This is the point of an auction: the seller gives buyers an incentive to reveal, through their bids, what they know about the prize’s value. The auction also, rather neatly, collects money on that basis.
The dragons should therefore consider what they might learn from each other’s bids. When casino owner Duncan Bannatyne offered to invest in a poker league, fellow dragon Richard Farleigh was quick to follow. If it was good enough for Bannatyne it was good enough for him.
These are familiar lessons to auction theorists such as Oxford professor Paul Klemperer. As one of the masterminds behind a mobile phone licence auction that raised ₤22.5bn, he presumably knows a thing or two about wringing cash out of investors, but he has also studied the way auctions reveal information. The person who wins an auction is the person who bid more than what everyone else thought the item was worth. In retrospect he is likely to be disappointed: economists call this “the winner’s curse”. Professor Klemperer argues that the curse has the ability to kill some auctions stone dead by discouraging sensible bidders from showing up at all.
The winner’s curse is especially severe when one dragon, such as Bannatyne, is a known expert. A rational dragon should never outbid the expert: if you’re paying more than the expert, you’re paying too much. Yet Bannatyne was, in fact, outbid. He may have made a mistake in expressing interest in a business where his expertise was evident to all. He could have instead offered a private deal later. Many real auctions end like this.
So what should a desperate entrepreneur do? To provoke an offer from the dragons, he or she should publicly commit to accepting dragon cash only if it is pledged inside the den; after the show is over, only outside investors will be considered. And to minimise the problem of expert dragons, the entrepreneur should insist on sealed bids, forcing the experts to make a serious competitive offer.
Of course, that would make for poor television - and in the show, dragons do indeed make rash offers against the counsel of game theory. Why aren’t they behaving rationally? Evan Davis, the BBC’s economics editor and presenter of Dragons’ Den, has a diplomatic explanation: “Economists are very clever and can get a long way with that cleverness, but nothing beats an intuitive judgment.”
