An auctioneer auctions a dollar bill at a starting bid of 5 cents, with a ‘simple’ condition – i.e., is both the highest and the second highest bidders pay. What then happens? It is a game devised by Martin Shubik of Yale University.
Imagine the first person bids 10 cents, thinking of pocketing a profit of 90 cents. But she is among a group of strangers, and another person, seeing the opportunity for an 85 gain, bids 15. Now, the first person can do two things – give up 10 cents and quit or continue bidding (perhaps 20 cents).
If she persists and the story repeats, a few interesting things can happen: 1) the auctioneer gets more than $1 (when the person bids for 55 cents and the previous one was 50 cents), 2) the highest bidder loses money (when she bids $1.05; more than the value of the bill).
A few more things can happen. One of them is the case when nobody bids. This is the best outcome in which no one loses (and gains!). The second possibility is for the first person to start at 5 cents and then form a coalition with the rest so that no one else bids. This results in a loss of 95 cents to the auctioneer. A third possibility is to raise the bid to 95 cents by the first person. This makes any subsequent offers unattractive.
Martin Shubik, The Dollar Auction game: a paradox in noncooperative behaviour and escalation. Journal of Conflict Resolution, 1971, 15 (1), 109-111
