Dollar auction game by game theory pioneer Martin Shubik

The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik, a pioneer of game theory,  to illustrate a paradox brought about by traditional rational choice theory in which players are compelled to make an ultimately irrational decision based completely on a sequence of apparently rational choices made throughout the game, also known as "escalation of commitment"
src wiki

A one dollar bill is put up for auction with the following rule: the bill goes to the winner, however the second bidder also loses the amount that he bids.

The winner can get a dollar for a mere 5 cents, but only if no one else enters into the bidding war. The second-highest bidder is the biggest loser by paying the top amount they bid without getting anything back. The game begins with one of the players bidding 5 cents (the minimum), hoping to make a 95-cent profit. They can be outbid by another player bidding 10 cents, as a 90-cent profit is still desirable. Similarly, another bidder may bid 15 cents, making an 85-cent profit. Meanwhile, the second bidder may attempt to convert their loss of 10 cents into a gain of 80 cents by bidding 20 cents, and so on. Every player has a choice of either paying for nothing or bidding 5 cents more on the dollar. Any bid beyond the value of a dollar is a loss for all bidders alike. A series of rational bids will reach and ultimately surpass one dollar as the bidders seek to minimize their losses. If the first bidder bids 95 cents, and the second bidder bids one dollar (for no net gain or loss), the first bidder stands to lose ninety five cents unless he bids $1.05, in which case they rationally bid more than the value of the item for sale (the dollar) in order to reduce their losses to only five cents. Bidding continues with the second highest bidder always losing more than the highest bidder and therefore always trying to become the high bidder. Only the auctioneer gets to profit in the end.

Shubik says it is not uncommon for the person conducting the game to end up with $3-5 for every dollar he auctions.

This theory is also known as "A Paradox in non cooperative behavior and escalation"


  1. If losing bid is forfeited then there is no incentive for players to even participate because then the game would be one sided in the favor of auctioneer. If there are two bidders then it would help if they have a secret understanding, let one of them bid for the dollar in 10 Cents (The second bidder) and rob the auctioneer of the rest 90 cents and share the profit equally.


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