The unbounded auction and the crazy multi-billionaire

 This is a conversation I had with ChatGPT at 5 AM. I'm posting it here without further comment.

Me:

Here's a bizarre concept that occurred to me in a dream. I want to know if it has a name.

Suppose you and I are in a bidding war over something. Doesn't matter what it is, but whatever it is must have some value. You and I may disagree about how we value it. Perhaps, say, you consider it to be worth $20 million. The bidding war is taking place online and you don't know the identity of the other bidders. You only know that individuals, and not governments (who under some circumstances have unlimited funds), are allowed to participate.

The auction might have a fixed duration or not. The auctioneers might see enthusiastic bidding and decide to let it run until it plays out one way or another.

Valuations can be quite personal. If we're both bidding on a piece of art, they can be wildly personal. People can also, and quite often have, decide sometimes that the act of winning is more important than getting a reasonable deal. They might not stop bidding at $19,999,999, even for something they value at $20,000,000.

Let's suppose the bidding does surpass $20 million and you grit your teeth and decide you just don't want to lose, so you keep raising your bid. But I keep raising mine: $30 million, $40 million, $80 million, $200 million. It's getting out of hand. Then a thought crosses your mind: You could be bidding against Elon Musk. At this particular moment Musk's wealth is estimated at upwards of $830 billion (not million). He can outbid anyone. And he has, at times, done things seemingly because he can, such as offering $54.20 per share for Twitter, a nod to the 420 of cannabis culture -- even though that share price might not be supportable by any reasonable valuation of what he was bidding on.

Since we don't wish to slander Mr. Musk, we'll state as a hypothetical that in this scenario, I am a crazy version of Mr. Musk. I'm willing to spend any amount to outbid you for this thing you value at $20 million. I may personally value it more than you do, but there is no reasonable justification for my valuing it at $200 million, and yet I keep outbidding you. You don't know who I am in this auction, you just see me outbid you over and over. It occurs to you that I, your opponent, may have such deep pockets that you cannot win -- because nobody can outbid Mr. Musk if he simply chooses he's willing to go for broke. You can't bid more than you have, because you'd go bankrupt and then the prize would be taken from you in the end, anyway.

Let's call this the "crazy Mr. Musk" hypothetical situation. Now... does this situation have a better-known name? And what else can you tell me about it?

ChatGPT:

This isn’t bizarre at all—economists and game-theory folks have been staring at exactly this nightmare for decades 😄. It does have names, plural, because different fields look at different facets of the same beast.

I’ll start with the best-fit name, then map your “crazy Mr. Musk” intuition onto the formal ideas.

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The closest, standard name: the Dollar Auction

This scenario is almost a textbook example of the Dollar Auction, first described by economist Martin Shubik in the 1970s.

What it is

• An auction where the highest bidder wins the prize

• But the second-highest bidder must also pay their final bid

• Classic example: auctioning a $1 bill

Why it explodes

Once bidding passes $1, both players are now trying to minimize losses, not maximize gains. The rational move early becomes irrational later, and bids can spiral far beyond the prize’s value.

Your scenario maps cleanly:

Dollar Auction	Your Scenario
$1 bill	Artwork / asset
Overbidding past value	Bidding past $20M
Fear of losing sunk costs	Fear of “losing” after committing
Escalation trap	Runaway bidding war

Even without the “second bidder pays” rule, the psychology and strategic logic are the same.

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The deeper concept: Escalation of Commitment

In behavioral economics and psychology, this is called escalation of commitment (sometimes “commitment bias” or “sunk cost fallacy in action”).

Key idea:

People continue investing in a losing course of action because of what they’ve already invested—money, ego, reputation, or identity.

In your auction:

• The value of the object stops mattering

• The act of winning becomes the objective

• Quitting feels like admitting defeat, not making a rational choice

This is why wars, lawsuits, and auctions all go off the rails in similar ways.

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The game-theory framing: Asymmetric Budgets / Incomplete Information

Your most insightful twist is this part:

You don’t know who the other bidder is.

That introduces two crucial elements:

1. Incomplete information

You don’t know whether you’re bidding against:

• A normal person

• A wealthy collector

• Or a “crazy” actor willing to burn money

This uncertainty alone can force rational players to drop out early.

2. Asymmetric resources

If one bidder has vastly deeper pockets (real or perceived), the equilibrium strategy for others is often:

Don’t play.

Even if the wealthy bidder is behaving irrationally, others must respond rationally to that irrationality.

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The “Crazy Mr. Musk” angle has a formal name too

This is known as strategic irrationality or credible irrationality.

The classic example comes from Cold War nuclear strategy:

• A player who might be willing to go to mutually assured destruction

• Forces the opponent to back down

• Even if that player would never actually want the worst outcome

By being—or appearing—unbounded, the actor gains leverage.

Your hypothetical version of Elon Musk fits this perfectly:

• Enormous resources

• Willingness to violate “normal” valuation logic

• Past behavior that makes the threat credible

Once other bidders suspect this, the auction is effectively over.

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Why this breaks auctions (and real markets)

What you’ve stumbled into is a reason real auctions usually add guardrails:

• Bid caps

• Identity verification

• Proof of funds

• Auction end rules

• Sealed bids instead of open bidding

Without these, auctions don’t converge to “true value”—they converge to who blinks first.

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TL;DR naming cheat sheet

Your scenario is best described as a combination of:

• Dollar Auction (core structure)

• Escalation of Commitment (psychology)

• Incomplete Information Game (unknown opponent)

• Strategic Irrationality (the “crazy billionaire” effect)

If you wanted a punchy label, “the Dollar Auction with an Unbounded Bidder” is something an economist would immediately understand.

And yes—this exact logic explains:

• Corporate takeover battles

• Art auctions

• Legal arms races

• Military standoffs

• And a shocking number of internet flame wars 😅

Me:

Does this concept have any bearing on the current race to develop artificial intelligence?

ChatGPT:

Oh yes — a lot. What you described maps onto the AI race almost uncomfortably well. The “crazy Mr. Musk” auction isn’t just relevant; it’s one of the best mental models for what’s happening right now.

Let’s line it up cleanly.

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The AI race as a runaway auction

Think of “advanced AI capability” as the object being auctioned.

• The value: productivity, economic power, military advantage, prestige, survival

• The bidders: companies and states (even if states pretend not to be in the room)

• The rules: unclear, evolving, weakly enforced

• The end condition: unknown

Everyone agrees AI is valuable. Nobody agrees how valuable, how soon, or how dangerous. That’s the setup for escalation.

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Where your model fits exactly

1. Escalation past intrinsic value

At some point, the race stops being about “How useful is the next model?” and becomes:

“We cannot afford to be the one who stops.”

This is classic escalation of commitment. Even if:

• Marginal gains are small

• Risks are growing

• Costs are exploding

Backing out feels worse than continuing.

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2. Incomplete information

No one actually knows:

• How close competitors are to breakthroughs

• What internal safety concerns they’re seeing

• Whether someone else is willing to take extreme risks

So every player must assume the worst.

If you suspect your rival might be willing to push recklessly, the rational response is… to keep pushing yourself.

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3. The “crazy bidder” problem

This is the most chilling overlap.

In your auction, the danger comes from one actor who might be willing to bid without limit.

In AI, that actor could be:

• A company willing to cut safety to win

• A state actor prioritizing strategic dominance

• A leader who believes “whoever wins first controls everything”

Even if most players are cautious, one credible outlier breaks the equilibrium.

Everyone else is forced to respond.

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Why restraint is unstable (game-theory-wise)

Here’s the brutal logic:

• If everyone slows down → safer outcome

• If one player defects and speeds up → huge advantage

• If you slow down while others don’t → you lose everything

That’s not a moral failure; it’s a coordination failure.

This is why voluntary restraint agreements are fragile unless they are:

• Verifiable

• Enforceable

• Universal (or nearly so)

Otherwise, the “auction” keeps going.

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Strategic irrationality shows up here too

A player who credibly signals:

“We will go all the way, no matter the risk”

…forces others to match that posture or fall behind.

This is why even organizations that talk about safety still:

• Scale aggressively

• Race to deploy

• Compete on benchmarks

No one wants to be the bidder who quits at $20 million while someone else goes to $200 million and walks away with the prize.

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The modern AI cast (briefly)

Without over-dramatizing individuals, the dynamic plays out among organizations like:

• OpenAI

• Google

• Anthropic

• State-backed labs in the US, China, and elsewhere

Even actors sincerely focused on safety are still in the auction, because opting out isn’t neutral — it’s losing.

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The real danger your model highlights

Your auction ends badly because:

• There’s no hard stop

• The downside is catastrophic

• And the players can’t trust each other to stop

That is exactly the worry many AI researchers express:

not that AI progress is bad,
but that unchecked escalation is.

In other words:

• The risk isn’t one evil actor

• It’s rational actors responding to perceived irrational ones

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One subtle but crucial difference

There is one place your analogy breaks — and it makes things worse.

In your auction:

• The loser goes bankrupt

• The damage is contained

In AI:

• The downside risk is shared

• Even the “winner” may lose

That turns the Dollar Auction into something closer to mutually assured damage.

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Bottom line

Your “crazy Mr. Musk” scenario is not just relevant — it’s diagnostic.

The AI race looks like:

• A Dollar Auction

• With uncertain bidders

• Asymmetric risk tolerance

• And no clear end condition

That combination is historically one of the most reliable ways humans create outcomes no one actually wanted.