Roland Dürre
Tuesday November 23rd, 2010

Game Theory – The One-EURO-Game.

The bank is selling 1 € at auction. The minimum bid is 0.01 €.

There is no minimum progress for bidders. So you are permitted to add 0.01 € as you bid.


The last bidder (the winner) and the one before last each pay the amount of their last bid to the bank.

1) The Euro sells for 0.40 €. The last bid before the end was 0.30 €. So the bank gets 0.70 € for the Euro. That is a loss of 0.30 €.

2) The Euro sells for 0.90 €. The last bid before was 0.85 €. So the bank gets 1.75 €. That is a profit of 0.75 €.

It seems that the bank has good chances of making a profit. The maximum profit possible for each auction is 99 cents (well, if bidders are extremely “unreasonable” – or if the Euro has a collector’s special value, there are, naturally, no upper limits).

But if the players are reasonable, all players will always contribute one additional cent. And the bank will then make a total profit of 99 Euros after 100 games.

Well, a nice game. But what do we learn from it?

Nothing! Or a lot? I do not know. Perhaps this is another nice mental game – but where is the meaning behind it?

(Translated by EG)


🙂 This article is part of my series “grumbling about the game theory”.

2 Kommentare zu “Game Theory – The One-EURO-Game.”

  1. E2E (Wednesday November 24th, 2010)

    Muß man nicht sagen “wenn die Spieler vernünftig sind und sich kennen”? Denn anders können sie sich ja nicht absprechen und abwechselnd ziehen. Aber lass es mal viele Spieler sein, die anonym entscheiden.
    Lass die Versteigerung im Internet sein und nicht nur 1 EUR, wo es offensichtlich ein Spiel ist. Die Bank versteigert täglich 10.000 EUR.
    Die Verlockung ist doch groß, die richtige Strategie (“Ich mache bei sowas nicht mit!”) nicht zu wählen.

  2. Chris Wood (Wednesday November 24th, 2010)

    Roland, your game theoretic analysis limps slightly.
    If just two people are still bidding, then each of them has effectively already lost what he has bid, (but he has a chance to get 1€). A bidder may now consider how to convince the second one that he will continue bidding whatever happens. If A has bid 1€, B may well bid 1½€ in order to frighten the competition, and limit his loss to ½€. The players have no better reason to stop bidding at 1€ than at any other sum that is small compared with what they own!
    If the game is going to be repeated 100 times, I may start with a minimum bid, but then always overbid the competition. The competition probably thinks I am crazy, and gives up. Of course if two players both use this strategy they will be ruined. But such a strategy cannot be dismissed as utterly stupid.
    This sort of thinking can be very dangerous in real-life situations, (consider Dr. Strangelove). It is good that we have game-theory to warn us.

    Poker involves similar but more complex calculations. One needs a strategy with a good random proportion. In addition one looks for signs in the opponents faces and tries to avoid giving such clues. I heard that one player had trouble with an artery in his neck, where his pulse showed. Some players should use masks.

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