The Game You Should Have Left

A lecture hall, some year around 1970. Martin Shubik is holding a dollar bill, and he is going to auction it. Highest bid wins the dollar. One further rule, stated once and then left alone: the second-highest bidder pays their final bid as well, and gets nothing for it.

Someone offers five cents. Someone else, ten. The room laughs; the dollar is cheap. By ninety cents the laughing has stopped, and two people are looking at each other across a room that has gone quiet, each holding a bid they cannot take back. At a dollar, the bill itself stops mattering. At a dollar five, the second bidder has to pick between a ninety-five-cent loss and a five-cent one. They bid. At three dollars forty, nobody in the room can say exactly when this became absurd, and both bidders are still in.

You are not in a lecture hall. But if two years of rising hours have left the number where it was, there is a reasonable chance you have spent most of that time in the second bidder’s chair, and that every single decision you made from it was correct.

That last clause is the whole piece. If the problem were only that effort had stopped converting, the fix would be the shape of the effort: which activities compound and which do not. That is a real failure with its own diagnosis. This is a different failure, and a worse one. The game you are in collects the runner-up’s bid. Whatever effort the loser put in is not returned. It is absorbed. In a game built that way, being the best bidder is exactly how you lose the most.

The rules, and why they hold you

Shubik published the game in the Journal of Conflict Resolution in 1971, under a title that gives the point away in advance: “The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation.” The rules, in his words: “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.”

Now read the arithmetic from the second chair. Your rival has bid ninety cents; you are at eighty-five. Stop, and eighty-five cents is gone. Bid ninety-five, and you might take a dollar for ninety-five cents, a five-cent profit. You bid. Your rival faces the same sum from the other side and goes to a dollar. You are at ninety-five, they are at a dollar. Stop, and ninety-five is gone. Bid a dollar five, and if they fold you lose only five. You bid.

Look at what just happened. The dollar has dropped out of the calculation. From the moment the bidding crosses one dollar, neither of you is bidding to gain anything. You are bidding to make your loss smaller, and every bid you make raises the loss the other person is now trying to make smaller. Shubik: “Once two bids have been obtained from the crowd, the paradox of escalation is real.” And his report from running it: “It is possible to ‘sell’ a dollar bill for considerably more than a dollar. A total of payments between three and five dollars is not uncommon.”

From the moment the bidding crosses one dollar, neither of you is bidding to gain anything. You are bidding to make your loss smaller, and every bid raises the loss the other person is trying to make smaller.

He closed the paper with the line that puts it in this piece rather than in a puzzle column: “This simple game is a paradigm for escalation. Once the contest has been joined, the odds are that the end will be a disaster to both.”

Not a sunk cost story, and that is why the usual cure fails

Nearly every retelling of the dollar auction reaches for the sunk cost fallacy. You keep bidding, the story goes, because of everything you have already put in. Too much invested to quit.

The explanation is wrong, and the error is expensive, because it prescribes a cure that has nothing to act on.

The sunk cost fallacy looks backward: you continue because of what you spent. Its cure is well rehearsed, and it works on genuine sunk-cost errors. Forget what you have spent. It is gone either way. Decide on the future alone.

Take that cure into Shubik’s room. Forget the ninety-five cents you have bid; it is gone either way. Decide on the future alone. What lies ahead: pay ninety-five by stopping, or put in a dollar five and perhaps pay five. The cure has touched nothing. What drove the next bid was never the money behind you. It was the smaller figure ahead of you, and that figure is real.

This is the part that catches the clever. Intelligence offers no protection against the dollar auction. Intelligence works out the marginal bid accurately, every time, and the marginal bid is always the correct one. The trap is not a failure of arithmetic. The arithmetic is the trap. Someone who reasons carefully about the next step, in a game where the next step is always locally right and cumulatively ruinous, reasons their way into a bigger bill than someone who got bored and walked out at forty cents.

Now carry that out of the lecture hall. The extra hour tonight is correct: the proposal is almost done, and stopping now wastes the six hours already in it. The extra hire is correct: the pipeline is nearly converting, and stopping now wastes the year already in it. The extra year is correct for the same reason, and so is the year after. Each decision, examined on its own, survives the examination. There is no single step where you made a mistake. There is a bid at every single step, in a game that pays the runner-up nothing.

That is the structure underneath “I am working harder and it is not converting.” Not laziness, not a discipline problem, not the shape of the effort. A payoff structure in which effort is the currency of the bid, the loser’s bid is collected, and each bid is rational. Call it what it is: an absorbing game.

Who keeps bidding: Staw’s experiment

Shubik’s game explains why the next bid is correct. It says nothing about why one person walks at forty cents and another is still bidding at three forty. For that, the second paper.

In 1976 Barry Staw, then at Northwestern, published a study in Organizational Behavior and Human Performance under the title “Knee-Deep in the Big Muddy.” He gave 240 business students at the University of Illinois a case. Each played the Financial Vice President of a fictional firm, Adams & Smith, in 1967, holding ten million dollars of research money to commit to one of two divisions, Consumer Products or Industrial Products. They chose, and wrote a paragraph defending the choice.

Then the case moved forward to 1972. Five years of financial results were on the table, and a further twenty million had to be allocated, this time in whatever split the subject liked. Half the subjects saw that the division they had picked had recovered. Half saw it had gone on declining while the other division improved.

The manipulation that matters is the second one. Half the subjects had made the 1967 choice themselves. The other half came to the case at 1972 and were told a previous financial officer had made the choice; they inherited it, with identical numbers.

The result, from Staw’s own tables. In every condition but one, the second allocation to the previously chosen division landed between eight and ten million: subjects whose choice had succeeded, subjects who had inherited a success, subjects who had inherited a failure. All of them put roughly nine million back in. The single exception was the group who had personally chosen the division and then watched it decline. They put in 13.07 million. The only significant difference Staw reports among the four conditions is that one cell, set against the rest.

Inheriting a failing decision did not make anyone escalate. Owning one did. The person who chose the game is the worst-placed person to decide whether to leave it.

Staw’s explanation is self-justification: the need, in his words, to “demonstrate the ultimate rationality of an original course of action.” Someone who inherited the choice can read the numbers as numbers. The author reads them as a judgement on the author, and meets the judgement with a larger bid.

Set the two papers side by side and the mechanism is complete. Shubik: inside an absorbing game, every next bid is locally correct. Staw: whoever entered the game bids hardest when it goes wrong, because each bid now defends the self that entered. The operator who picked the market, the model, the role, the flagship project, is not just one more bidder in this auction. Of everyone in the room, they have the most reason never to stop.

The runner-up test

Not every hard game is an absorbing one. A hard game can also be a dip: the runner-up’s bid buys something that compounds even when the round is lost. So the first diagnostic is not “is this difficult” but something narrower.

Does the runner-up keep their bid?

In a sales pipeline that works, a lost deal hands back the relationship, the objection you now know how to answer, the reference you can still ask for. The bid comes back, in part. In a dollar auction the lost bid hands back nothing. That is the whole definition of absorbing.

Run it on the games you are actually in. The hours poured into the proposal that lost: what came back? The year in the channel that did not convert: what came back? The year and a half spent building the capability the market never bought: what is left in your hands now that the round is over? Sometimes the honest answer is a real asset, a skill, a relationship, a system that will carry weight in the next round. Then you were in a dip, and effort was the right currency. But if the honest answer is “nothing, except the knowledge that I was close”, you have just given the definition of an absorbing game, from the second bidder’s chair. Close is what the second bidder always is. Close is exactly what a dollar five feels like.

The exit is decided before the first bid

So how do you get out?

The instinctive answer is courage: simply stop bidding. That is an answer to an easier question than the auction is asking. Stopping mid-auction crystallises the loss. It is the one move that turns a running bill into a settled one, and by construction the next bid looks cheaper than that bill. Courage against arithmetic loses most of the time, and it deserves to.

The better answer comes from a third paper. In 1986 Barry O’Neill, writing in the same journal Shubik had used, asked what a fully rational player would do in the dollar auction if the budgets were finite and known. His result turns the game around. With known budgets there is a rational solution, and it is not “bid carefully.” The first player opens with one specific bid, sized to the budget, and the second player stays silent. Rational players, O’Neill showed, would not bid against each other at all. His contrast was with the prisoner’s dilemma: the dollar auction is not a trap by nature. It works on one particular error in the bidders, the error of entering without a budget.

Read that as an operating rule and it says three things.

First: mid-auction there is no winning move. Only a smaller loss. Any strategy that begins after the second bid is a strategy for losing less, and you should name it as that rather than dress it up as a comeback.

Second: the winning move is either the opening bid or silence. Set the budget before you enter. Not a hope, a number: this many months, this much cash, this many hours of the one person the business cannot replace. Set the walk-away line at the same time, in writing, before the first bid has made the line look like cowardice.

Third, and this is the one Staw adds: do not hold the line yourself. The author of the entry escalates hardest when the game turns. That is not a character flaw; Staw’s subjects were ordinary business students, and the inheritors in the same room read the same numbers correctly. So hand the decision to stop to a person who did not choose the game. A board member who was never in the room. An advisor with no authorship. A written rule that someone with low responsibility for the entry is allowed to enforce. In Staw’s design, low responsibility brought the allocation down from thirteen million to nine. That condition can be built on purpose.

There is no winning move mid-auction. There is only a smaller loss, and the next bid will always look cheaper than the bill you would pay by stopping.

Where this reaches, and where it does not

Everything above describes a payoff structure, nothing more. It reaches every situation that carries the structure: a runner-up who pays, bids that are locally rational, an author who defends the entry. It does not reach the cases where the structure only appears to be present.

The dip is the honest limit. Some games fail the runner-up test in a given round and still pay the runner-up over time, because the losing bid bought a capability that compounds. A first product that did not sell but taught the team how to build the second. A market that did not open but produced the three relationships that opened the next one. The runner-up test cannot cleanly separate a bid that was absorbed from a bid that purchased a skill, and no test I know of can. The narrower instruction I can defend: if you cannot name, in a single sentence and to a person who had no hand in choosing the game, the capability the losing bid bought, treat it as absorbed. That leaves a real objection standing. Some of you are in a dip, and this piece will read as a reason to leave too early. The framework is incomplete on that boundary, and I would rather say so than sell you a test that is cleaner than it is.

The prize was a dollar

The auction explains one more thing, and it is the part that gets misread as ingratitude.

Competitive bidding has a well-known result called the winner’s curse: the winner is the party who most overvalued the prize. Win the dollar auction and what you hold is a dollar that cost you four. What follows is not triumph. It is a specific flatness, the recognition that the arithmetic you refused to run at the start has now been run for you.

That is one of the quieter shapes of Success Anhedonia: the milestone arrives, the number is finally hit, and nothing happens inside. The usual explanation is a problem of meaning. Sometimes it is simply the bill. You won an absorbing game, and the prize was always a dollar. The flatness is accurate.

What to hold onto

One question to run before you close this tab, and it is the only one the auction actually asks: would you enter this game today, at this price, with everything you now know?

If the honest answer is no, then every bid from here on is placed in a game you have already ruled out. That is not a reason to feel foolish. It is the first accurate reading of the board.

Kasimir Hedstrom | MindMastery