“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 in 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.” John Kay, ‘Kipling’s game theory lessons for Greece’, Financial Times, July 27, 2011
In such a game, offers will quickly escalate towards a dollar, with the highest bid at 99 cents and the underbid at 98 cents. At this point it pays the underbidder to to offer a dollar. He makes no gain but avoids a loss of 98 cents. This game, however, will not stop there. It now pays the underbidder to bid $1.01, converting a loss of 99 cents to one of a single cent. And so the plays continue. The underbidder always comes back to avert a greater loss. The game eventually may end, but never well for any participant. There are reports that over $200 has been paid for a single dollar in Shubik’s game.
Shubik proposed the paradox as a problem to which game theory offers no solution. However, there is a solution if one perceives the nature of the game in time. Avoid like the plague situations that mimic the structure of this game. The great English poet, Rudyard Kipling, anticipated Shubik’s paradox and resolved it with respect to pre-Norman England:
“We’ve proved it again and again,
that if once you paid him dane-geld,
you never get rid of the Dane.”
So the United Kingdom was prescient in refusing to join the Euro-zone. For the Danes are now located in the south of Europe, not the north. They are called the PIIGS. And the Euro-zone is locked into the Shubik dollar bill auction:
“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 to a permanent underwriting of the Greek economy, than to risk the breakdown of European economic integration” John Kay, ibid.
At this point I depart from the usually impeccable logic of John Kay. Immediately one perceives the nature of this game, it pays everyone to quit the game, including the random winner. So it is wise for Germany to quit the Euro-zone now. It was wise for the Bush administration to allow Lehman Brothers to die, it was wise of Margaret Thatcher to confront the British miners in a bloody 18 month confrontation, it will be wise for the GOP to confront its right-wing tail and for the Democratic Party to confront its left-wing tail in order to maintain the financial integrity of U.S. government debt in international markets.
Take one’s money off the table before the Danes take it all. That is Rudyard Kipling’s message and the warning to us all in this era of increasingly arrogant Viking invasions. There is no point in playing the game and hoping Canute-like, that the rules will change and that the tides will turn according to your wishes. For assuredly, that will never happen while the dane-geld remains on the table.
Tags: Martin Shubik's doillar bill auction game, a game that should never be played, Rudyard Kipling tells us the way to go, Danes always pursue dane-geld when it is available, poet rudyard kipling, game theory, greek economy, John Kay