The Dollar Auction game: a paradox in noncooperative behavior and escalation

Abstract

There is an extremely simple, highly amusing, and instructive parlor game which can be played at any party by arranging for the auction of a dollar. This game illustrates some of the difficulties with the noncooperative equilibrium concept and games in extensive form (von Neuman and Morgenstern, 1945). The game is simplicity itself and is usually highly profitable to its promoter. The auctioneer auctions off a dollar bill to the highest bidder, with the understanding that both the highest bidder and the second highest bidder will pay. For example, if A has bid 10 cents and B has bid 15 cents, then the auctioneer will obtain 25 cents, pay a dollar to B, and A will be out 10 cents. Suppose that bids must be made in multiples of 5 cents. Furthermore, suppose that the game ends if no one bids for a specific length of time. Ties are resolved in favor of the bidder closest to the auctioneer. These rules completely specify the game except for a finite end rule; i.e., as specified, bidding could conceivably never cease. We could add an upper limit to the amount that anyone is permitted to bid. However, the analysis is confined to the (possibly infinite) game without a specific termination point, as no

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