Some traps do not need to hide their rules. On the contrary: they work precisely because everyone can see the rules, and once you are inside, each small step seems reasonable.

The Bid That Crosses One Euro

Strategist
Master plays

Riddle statement

A €1 coin is being auctioned. The highest bid wins the coin, but both the winner and the second-highest bidder must pay their last bid.

Ana has bid €0.99 and is winning. Bruno has bid €0.98.

Bruno can drop out and lose his €0.98, or raise the bid to €1.

Why might it seem rational for him to raise? And how does the same logic push the bids above the value of the coin?

Show solution

Solution

If Bruno drops out, he loses €0.98 for certain and receives nothing.

If he raises to €1, he becomes the provisional winner. If Ana drops out, Bruno pays €1 and receives a €1 coin: his net result is 0. Raising gives him a better way out than the certain loss of €0.98.

But now Ana is second with a bid of €0.99. If she drops out, she loses that €0.99. If she raises to €1.01 and Bruno drops out, she wins the coin and her net loss is only €0.01.

The same comparison repeats at each turn. The players stop deciding whether the coin is worth the new bid and start deciding whether they prefer a small additional loss or making their accumulated loss final.

That is why the bid can cross €1 and keep rising. Each local decision looks defensive, even though the whole sequence is ruinous.

Answer: Bruno raises to avoid a certain loss; the same pressure then passes to Ana and causes the escalation.