Dollar Auction Problem: The price of your stupidity (part 1)

Economist Martin Shubik’s Dollar Auction Problem has been on my mind ever since someone mentioned it to me. It’s a simple game with surprising consequences, and the more I think about it, the more I see it everywhere.

Let’s talk about what makes this little experiment so fascinating—and why it might hit closer to home than you’d expect.

Here’s how it works:

You’re in an auction with one opponent to win a $100. The opponent starts by bidding $1 for the $100 note. If you win, you pay your last bid but gain $100. However, the loser also loses the value of their last bid. For example, if you bid $2 and your opponent stops, they lose $1, and you gain $98 ($100 – $2).

What would be your betting strategy?

I took a dig at the problem and here it goes. Let’s break down the problem through scenarios and strategies.

Strategy 1: Tire the Rookie

This approach focuses on wearing down your opponent through successive bids, increasing their potential loss and hoping they fold. Here’s how it plays out:

• Opponent bids $1.

• You bid $2.

• They bid $3.

• You bid $4.

• And so on……

What happens with each bid?

• Your potential profit decreases as your bid rises.

• Your prospective loss increases.

• Your opponent’s prospective loss also increases if they make the next bet, forcing them to decide whether to stay in the game or concede.

At some point your hope is that your opponent chickens out.

Now this trick is probably going to work with only the greenest of rookies (which even I am not and I failed third grade) so the bar is abysmally low for someone to fall into this trap.

Strategy 2: Jump the Gun and Try to Win

Now this strategy was my System 1 answer (Robert Greene has been popping up in my feed a lot quite lately, and I suspect this approach being my first one, may be a consequence of me internalising some of his content.)

Here’s the strategy:

• Opponent bids $1.

• You immediately bid $99.

Now the reasoning behind this though is deeper and something that I believe I borrowed from Prospect theory by Kahneman (whose theory I would like to believe is part of my system 1).

Let’s say your opponent bids $1 and you bid $99,

Now, If your opponent decides to bet they will have to bet $100.

The bet of $100 dollars means 2 things:

1. They are breaking even.

2. They are setting themselves up to potentially lose $100 or more.

For your opponent, their previous prospective loss while making your first bet was $1 and now with this bet it is $100 or more. How many people do you think will probabilistically take that bet? Well Daniel Kahneman had something to say on that with Prospect theory.

We will break down how it applies here but before that, turn the tables around and ask yourself if you were in your opponent’s position would you bet a $100?

Regardless of what your answer was to the above question (in theory), here is why most people won’t make that bet (in practice) according to Prospect theory.

• Reference point: People make decisions relative to a reference point, which is often their current state or status quo. Consider our situation, when the opponent has to make the $100 dollar bet, these are their options:

  • Don’t bet - lose $1

  • Bet - lose $100 or more

The sudden jump in prospective loss from $1 to $100 or more is so high that most folks won’t make the bet when they are playing in the real world according to Prospect theory.

• Loss aversion: People tend to prefer avoiding losses over acquiring equivalent gains. This is because people assign more psychological weight to outcomes that they can characterize with greater certainty.
  
  Let’s adapt it to our context. A $1 loss is a certainty, if your opponent does not take the bet, but if your opponent does take the bet, then the possibility of losses increases. Added to this is the consideration that you really are not making any profit anyway.

Now with these two in mind, estimate the probability of your opponent making the $100 dollar bet.

If your opponent STILL bets $100 I have news for you, either one or more of the following five scenarios are likely.

• They are playing in theory

• They are psychopaths

• They don’t like you

• They have a trust fund. (Think Man in Finance, 6’5, trust fund, blue eyes?)

• They are stupid.

Now at this point you probably are going to ask me, what happens if they bet $100 dollars?

Before I tell you what I would do, let me give you the ACTUAL answer of the auction problem (spoiler alert).

The Economist’s Answer

Economist Martin Shubik conceptualized this Dollar Auction problem to illustrate how individuals succumb to the sunk cost fallacy. His recommended strategy? Don’t engage in the auction at all. If you’re already playing, the optimal strategy is to keep betting, (even if it means betting your entire net worth).

Shubik’s point is to highlight irrational decision-making—how humans often make choices based on sunk costs rather than rational outcomes.

Your opponent has bet $100 dollars and you have just been told by an economist that this was a theoretical experiment all along to highlight how irrational human beings are. What do you do?

Embrace Practicality

• Acceptance: Acknowledge that you’re in a losing game and will lose money. Yes, it was unwise to play in the first place.

• Set a Stop Loss: Decide on a maximum bid where you’ll cut your losses and exit. For example, if your stop loss is $130, you stop bidding at that point, no matter what.

Now I know he says the optimum strategy is to keep betting. But as someone who has traded the markets without a stop loss (the confidence of a 19 year old, excuse me) and has lost quite a bit of money to give me lifelong trauma, I will leave you with just one disclaimer: Don’t try what he says at home.

Now as for the remaining strategies, I will need to do some reading and refine them before I write about it. Stay tuned for part 2! :)

But to sum up what we have so far, into a little self help lesson for the new year:

The Dollar Auction isn’t just an experiment—it’s a reflection of how we handle life’s trickiest moments. Whether it’s pouring money into a plummeting stock (unless you’ve got insider information, of course) or clinging to a two-year “talkingship” just because he remembers your birthday, the more you invest, the greater the losses. The longer you stick around, the harder it becomes to let go, and the more damaging the consequences become.

As we paddle into the New Year, maybe it’s time to stop clinging to that lifejacket full of holes—aka the sunk cost fallacy. Sure, you’ve invested in it, but holding on just makes you sink faster. Sometimes, the smartest move is to ditch the soggy vest and swim toward something that actually floats.

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In my upcoming essays in this series, I’ll explore:

1. Dollar Auction Problem (part 2): Incorporating insights from external sources and revisiting concepts from Daniel Kahneman’s Thinking, Fast and Slow to develop refined strategies that balance profit and risk for the Dollar Auction Problem.

2. The Elixir of a Trader: Stop Loss: Applications in life, relationships, and financial decisions.