Dollar auction
The dollar auction , also commonly known as the escalation auction , is a game developed by Martin Shubik which, thanks to its gameplay, lets participants act irrationally, even though they actually have all the information they need to behave rationally . Thus, this game calls into question the applicability of the " theory of rational decision " in relation to human behavior. The content of this game is the auction of one US dollar .
Gameplay
An auctioneer offers two or more bidders a dollar for auction. The first bidder places a bid for the dollar, e.g. B. 1 cent. The next bidder may bid more than the previous one or nothing at all. The auction ends when no bidder raises his predecessor's bid. The bidder with the highest bid gets the dollar. This winner and the participant with the second highest bid pay their respective bid amount to the auctioneer.
procedure
The auction usually runs as follows:
The participants outbid each other by a few cents to secure the dollar. The bids rise until the one-dollar limit is reached, because a winning bid of 99 cents still brings a profit.
The following process is interesting. The auction usually does not stop when the one-dollar bid is reached. The bids rise to an average of $ 3.40. This escalation, which is financially disadvantageous for the bidders, can be explained by a short-sighted decision, i.e. one that only considers the next moves, not all moves until the end of the game:
Suppose there are two bidders A and B and A's current - not first - bid is 99 cents. B, with the second highest bid of z. B. 98 cents, you have to choose not to submit another bid and certainly lose 98 cents or bid a dollar and get the chance to win the auction and thus the dollar. Usually B offers a dollar. If A did not bid any further, he would be obliged to pay his last bid of 99 cents. But if he bids $ 1.01 and B makes no further offer, A would get the dollar and lose only one cent. When choosing between a safe loss of 99 cents or an uncertain, smaller loss, most participants choose the second option and thus bid $ 1.01. Now B is faced with the choice of losing a dollar with certainty or bidding more for the prospect of a smaller loss.
As the game progresses, the loss for both players increases. From a certain phase onwards, the profit or the amount of the loss takes a back seat and it is then about winning the auction and no longer about the payout itself. The opponents begin to accuse each other of acting irrationally. The game shows the character of an escalation. You don't want to be the fool who loses.
Counter-strategies
One way to prevent an escalation and bring the bidders a profit is to work together . This assumes that an agreement is possible and will take place before or during the auction. This arrangement could look like this: One participant offers a cent and suggests that the rest of the players share the profit if they do not place any bids. As a rule, this only works for a small number of bidders.
Another possibility is for the first bidder to bid 99 cents at the very beginning. For a subsequent bidder, "no bid" is then a weakly dominant strategy . The first bidder then has one cent as profit. However, if someone continues to bid, you will fall into the trap already mentioned. In the two-bidder auction, this trap is avoided if the first bid is exactly one dollar. The profit is then zero, but "no bid" is then a strictly dominant strategy for every other bidder .
Another possibility is not to take part in the game, but you cannot win anything.
Web links
- Further information and analyzes (PDF file; 63 kB)
Individual evidence
- ^ Martin Shubik (1971), " The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation (PDF; 375 kB)," The Journal of Conflict Resolution , 15 (1), pp. 109-111.
- ↑ William Poundstone, Prisoner's Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb , Anchor / Random House, 1993, especially Chapter 13: "The Dollar Auction" (in English)