Thursday, April 15, 2004
The trouble with Dollar Auctions
An e-mail from Kuldeep reminded me that I needed to link to one of the best posts that Atanu has made in recent times. In a post on Dollar Auctions, he uses the framework of the dollar auction model to explain wars and much else. Though I have excerpted some of the stuff on here, I would strongly recommend you read the rest of it. It's a brilliant and thought-provoking post.
One enlightening model of human behavior is the so-called "Dollar Auction" which illustrates the sort of trap that conflicts can lead to with costly consequences. This auction proceeds much as a normal auction except that while the highest bidder gets to keep the $1 bill bid upon, the second highest bidder has to pay the auctioneer the amount of the second highest bid.
This game played at a party leads to some unexpected outcomes which result from the dynamics of conflict escalation. Players exhibit irrationality in most cases and often the $1 bill is auctioned off for many times its value. This happens because there is a trap in the structure of the game where the loser not only does not get the prize but also loses the amount he bid.
Suppose the auction begins with a bid of 5 cents. This is appealing to most since 5 cents is worth bidding for a prize of a dollar. But as the bidding proceeds beyond 50 cents, the players are caught in a trap. At this point the game changes complexion. Assuming that bids have an increment of 5 cents, the person with the bid of 50 cents has an incentive to outbid the higher bid of 55 cents. Otherwise he would lose 50 cents and the winner would gain 45 cents. Naturally, the bidding continues upwards. The auctioneer from this point onwards stands to gain irrespective of what happens next. When the highest bid is 95 cents, the situation is not at all rosy for the second highest bidder. He stands to lose 90 cents if he stops there. He also knows that his opponent stands gain 5 cents. Therefore the bid reaches $1. The participants quickly realize that it is no longer a game in which either of them would win. The question from then on is whether one can stand to see one's opponent lose less than oneself. Because at this point both lose money but the "winner" loses a dollar less than the loser. The only winner in this game is the auctioneer.
What are the modes of termination of the dollar auction? First, the players could realize right up front the nature of the trap and refuse to participate. No one loses and the auctioneer doesn't gain anything. Once the auction starts, it is still possible for the players to exit without losing. This happens if the players collude and decide to not outbid each other and to stop before the highest bid reaches 50 cents. They could agree to split the profits among themselves. And the auctioneer loses money in this deal. This scenario does not occur because co-operation requires accomodating one's opponent's interests which may be inconceivable in a situation of escalating conflict. Once past the 50 cent mark, the auctioneer is assured of a profit. The game continues till one of the participants exhausts his capacity to bid any more or one decides to cut his losses and fold. The winner is of course not as badly off but still has the winner's curse of having paid more than the value of the prize to win the prize.
The only way to win at a dollar auction therefore is either to not participate or if one does begin, then to either reach a compromise with one's opponent or to exit as early in the game as possible. Wars too have the peculiar characteristic that both parties, winner as well as the loser, pay. The dollar auction game illustrates the trap that nations fall into in a process of conflict escalation given the structure of strategic games.
One enlightening model of human behavior is the so-called "Dollar Auction" which illustrates the sort of trap that conflicts can lead to with costly consequences. This auction proceeds much as a normal auction except that while the highest bidder gets to keep the $1 bill bid upon, the second highest bidder has to pay the auctioneer the amount of the second highest bid.
This game played at a party leads to some unexpected outcomes which result from the dynamics of conflict escalation. Players exhibit irrationality in most cases and often the $1 bill is auctioned off for many times its value. This happens because there is a trap in the structure of the game where the loser not only does not get the prize but also loses the amount he bid.
Suppose the auction begins with a bid of 5 cents. This is appealing to most since 5 cents is worth bidding for a prize of a dollar. But as the bidding proceeds beyond 50 cents, the players are caught in a trap. At this point the game changes complexion. Assuming that bids have an increment of 5 cents, the person with the bid of 50 cents has an incentive to outbid the higher bid of 55 cents. Otherwise he would lose 50 cents and the winner would gain 45 cents. Naturally, the bidding continues upwards. The auctioneer from this point onwards stands to gain irrespective of what happens next. When the highest bid is 95 cents, the situation is not at all rosy for the second highest bidder. He stands to lose 90 cents if he stops there. He also knows that his opponent stands gain 5 cents. Therefore the bid reaches $1. The participants quickly realize that it is no longer a game in which either of them would win. The question from then on is whether one can stand to see one's opponent lose less than oneself. Because at this point both lose money but the "winner" loses a dollar less than the loser. The only winner in this game is the auctioneer.
What are the modes of termination of the dollar auction? First, the players could realize right up front the nature of the trap and refuse to participate. No one loses and the auctioneer doesn't gain anything. Once the auction starts, it is still possible for the players to exit without losing. This happens if the players collude and decide to not outbid each other and to stop before the highest bid reaches 50 cents. They could agree to split the profits among themselves. And the auctioneer loses money in this deal. This scenario does not occur because co-operation requires accomodating one's opponent's interests which may be inconceivable in a situation of escalating conflict. Once past the 50 cent mark, the auctioneer is assured of a profit. The game continues till one of the participants exhausts his capacity to bid any more or one decides to cut his losses and fold. The winner is of course not as badly off but still has the winner's curse of having paid more than the value of the prize to win the prize.
The only way to win at a dollar auction therefore is either to not participate or if one does begin, then to either reach a compromise with one's opponent or to exit as early in the game as possible. Wars too have the peculiar characteristic that both parties, winner as well as the loser, pay. The dollar auction game illustrates the trap that nations fall into in a process of conflict escalation given the structure of strategic games.
