Kipling’s game theory lessons for Greece

by John Kay

Financial Times
July 26, 2011

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.

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