The game theorist Martin Shubik invented an unpleasant economists’ party game called the dollar bill auction. The players agree to auction a dollar bill with one cent increments to the bids. As usual, the dollar goes to the highest bidder. The twist is that both the highest bidder and the second-highest bidder must pay.
You might start with a low bid – but offers will quickly rise towards a dollar. Soon the highest bid will be 99 cents with the underbidder at 98 cents. At that point, it pays the underbidder to offer a dollar. He will not now gain from the transaction, but that outcome is better than the loss of 98 cents. And now there is a sting in the tail. There is no reason why the bidding should stop at a dollar. The new underbidder stands to lose 99 cents. But if a bid of $1.01 is successful, he can reduce his loss to a single cent.
The underbidder always comes back. So the auction can continue until the resources of the players are exhausted. The game must end, but never well. There are reports that over $200 has been paid for a dollar in Shubik’s game. That would be a contender for the most valuable dollar bill in existence had not $43m been paid for Andy Warhol’s representation of 200 of them.
You might resolve not to enter such an auction. Perhaps, but if everyone takes that sensible line a dollar bill will be there for the taking. Shubik proposed the paradox as a problem to which game theory offered no solution. You may by now have resolved not to mix socially with economists – if you had not made that decision already. And that is exactly the right answer. Avoid situations that mimic the structure of this game.
However, this is not so easy. The essence of Shubik’s problem is that it always seems worthwhile to offer a small amount to avert a larger loss. It is plainly better to write down Greece’s debt, even to agree a permanent underwriting of the Greek economy, than to risk the breakdown of European economic integration. It would have been far less expensive to assume the costs of a rescue of Lehman than to bear the costs of a near collapse of the global financial system. It is manifestly preferable to make concessions to the Republican right than to risk the consequences of a US debt default.
In the same way, it seemed more sensible to meet the demands of striking miners than to contemplate the shutdown of large sections of British industry. More humane to give in to the demands of hijackers than to risk loss of innocent life. Always better to spend a little more to complete a project whose budget has overrun. Sensible to pay off Somali pirates. And absurd to plunge the world into war over a territorial dispute in “a far off country of which we know nothing”.
So we must reaffirm the political will to defend European unity at any price. We should take the advice of Larry Summers, offered in this paper only last week, to make a commitment to prevent the collapse of any global financial institution. We must put the integrity of the US fiscal system ahead of partisan political considerations. Like it or not, we are in the dollar bill auction and must stay for as long as it takes.
But, as in the dollar bill auction, so it is in business, politics and finance: the underbidder always comes back. Rudyard Kipling anticipated Shubik’s conclusion: “We’ve proved it again and again, that if once you have paid him the dane-geld, you never get rid of the Dane.” Today, the Danes are in the south of Europe, not the north; the greedy coastal raiders of Viking times are now the officers and traders of investment banks; the Tea Party warriors enjoy the fanaticism that comes from the certainty that they are right. The underbidder always comes back.
In the dollar bill auction, one party eventually scores a pyrrhic victory and takes possession of the dollar bill. Both parties lose, but the smaller loser is the person who sticks out longest. That is not usually the rational player.
