Cheating for a $20


Each year in my 500-student principles class I gather a group of eight students and tell them that I will auction a $20 bill to the highest bidder. If two or more students bid the same thing, the difference between $20 and their joint bid will be divided among the winning bidders. They can collude to fix the price just like oligopolists who violate antitrust laws, but they must mark down their bids in secret.

Today seven of the students stuck to the collusive agreement, and each bid $.01. They figured they would split the $20 eight ways, netting $2.49 each. Ashley, bless her heart, broke the agreement, bid $0.05, and collected $19.95. The other 7 students booed her, but I got the class to join me in applauding her, as she was the only one who understood the game.

It showed that, even in a market like this one with very few players, collusion is difficult to maintain. There are tremendous incentives for one or more parties to cheat and move the market toward a competitive outcome. Unfortunately nobody has ever gone as high as the predicted equilibrium bid of $17.50.


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  1. KW says:

    Long live the Ashleys -they’ll create jobs for our children.

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  2. Joey says:

    I’m skipping my Game Theory class as I read this…

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  3. nate says:

    why would the equilibrium bid be 17.50? i would think it would be 19.99

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  4. rda says:

    Is being known as the “cheater” in a class of 500 worth $20?

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  5. relaxing says:

    The exercise only says the stakes weren’t high enough for those colluding to engage in extortion or violence.

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  6. Silas Barta says:

    No, she learned how to game a very narrow instance of that type of scenario, and got lucky that someone else didn’t bid $0.06.

    Try that kind of thing in real life, and you’ll get the social equivalent of a horse’s head in your bed.

    Incidentally, how many friends did Ashley make out of this event?

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  7. Imad Qureshi says:

    Well Ashley was able to do this because this is not a multi period game. Ashley would have cooperated if this was a multi period game and there was a different way where other seven players could harm her (in a different game may be). There was an absence of threat which made it possible for her to cheat.

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  8. Howard says:

    “KW” you are oversimplifying. The pursuit of money does not always create jobs.

    I for one will neither applaud nor deride Ashley. Greed is as much a part of the human condition as happiness/sadness.

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