# Schelling's Game Theory: How to Make Decisions

By Robert V. Dodge | Go to book overview

CHAPTER 10
The Dollar Auction

The dollar auction is a game that models two interrelated phenomena: escalation and sunk cost. It has transparent relevance in contemporary society and is a deceptively simple game that is generally remembered once it has been played. Its lesson is clear and offers a warning to be alert to certain specific considerations in a variety of situations.

A dollar is offered for auction to be sold to the highest bidder. One condition of the auction is that both the highest bidder and the second highest bidder must pay the amount of their final bids. For example, if the highest bid ended up being \$.25, and the second highest bid was \$.20, the highest bidder would pay the auctioneer \$.25 and receive the dollar, and the second highest bidder would pay the auctioneer \$.20 but receive nothing. A second condition is that no communication is allowed among bidders so no collusion is possible.

Generally, this innocuous game of selling a dollar for bids begins at five cents with bidding in the same small units. It usually seems comical when the bidding begins, but the humor fades as reality sets in. There is a serious trap in this. Typically, the dollar auction proceeds as follows: Someone makes the opening five cent bid, which is quickly raised by other bidders. At this stage the participants commonly are taking part in a spirit of fun or possibly hoping to get a cheap dollar from a foolish teacher, and are not seriously considering the consequences of their bidding. For illustrative purposes, say the opening bid is \$.05 by bidder X. Bidder Y raises it to \$.10, followed by a bid of \$.15 by bidder Z. X ups it to \$.20, Y to \$.25, Z to \$.30, and then X to bids \$.35.

At this point things are often happening quickly and it may still appear to the bidders that the auctioneer was foolish to offer to sell the dollar, but the participants are beginning to realize they stand to lose money if they do not win in the bidding. Perhaps Y, being the low bidder at this point, will drop out, since it will cost him nothing. This leaves X bidding against Z. Z also could drop out at this point, but it would cost him \$.30, while upping the bid only \$.05 might get him the dollar. So Z raises the bid, thus putting X in the same situation at a more costly level (X would lose \$.35 by dropping out). When one bidder reaches \$.50, if the other raises the bid, the auctioneer is guaranteed a profit.

The trap in the Dollar Auction is that at each round a participant has more and more to lose by not raising the stakes. Bidding is usually reduced to two

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