Game Theory Is Really Counterintuitive

Every now and then, I hear someone say that game theory doesn’t tell us anything we don’t already know. In a sense, they are right—game theory is a methodology, so it’s not really telling us anything that our assumptions are not. However, I challenge someone to tell me that they would have believed most of the things below if we didn’t have formal modeling.

  • People often take aggressive postures that lead to mutually bad outcomes even though mutual cooperation is mutually preferable. Source.
  • Even if everyone agrees that an outcome is everyone’s favorite, they might not get that outcome. Source.
  • Sometimes having fewer options is better than having more options. Source.
  • On a penalty kick, soccer players might wish to kick more frequently toward their weaker side as their weaker side becomes increasingly inaccurate. Source.
  • In a duel, both gunslingers should shoot at the same time, even if one is a worse shot and would seem to benefit by walking closer to his target. Source.
  • There’s a reason why gas stations are on the same corner and politicians adopt very similar platforms. And it’s the same reason. Source.
  • Closing roads can improve everyone’s commute time. Source.
  • Fewer witnesses to a crime might be preferable to more. Source.
  • You should bid how much you value the good at stake in a second price auction. Source.
  • If you pay the value you think something is worth, you are going to end up with a negative net profit. Source.
  • Lighting money on fire is often profitable. Source.
  • Going to college can be valuable even if college doesn’t teach you anything. Source.
  • An animal might be better off jumping high in the air repeatedly than running away from a predator. Source.
  • Knowing just slightly more about the value of your car than a potential buyer can make it impossible to sell it. Source.
  • Nigerian email scammers should say they are from Nigeria even though just about everyone is familiar with the scam. Source.
  • Everyone might mimic everyone else just because two people chose to do the same thing. Source.
  • A biased media may be better than an unbiased media. Source.
  • Every voting system is manipulable. Source.
  • You might want to abstain from voting even though you strictly prefer one candidate to another. Source.
  • Unanimous jury rulings are more likely to convict the innocent than simple majority rule if jurors vote intelligently. Source.
  • The House of Representatives caters to the median member of the majority party, not the median member of the institution overall. Source.
  • Plurality, first-past-the-post voting leads to two-party systems. Source.
  • United Nations Security Council members sometimes do not veto resolutions even though they strongly dislike them. Source.
  • Without the ability to propose offers, you receive very few benefits from bargaining. Source.
  • Settlements always exist that are mutually preferable to war. Source.
  • Fighting wars removes the need for war. Source.
  • You might want to shoot to miss in war. Source.
  • Nonproliferation agreements can be credible. Source.
  • Weapons inspections are useful even if they never find anything. Source.
  • Economic sanctions are useful even though they often fail in application. Source.
  • Pitchers shouldn’t change their pitch selection with a runner on third base, even though curveballs are more likely to result in wild pitches. Source.
  • Sports teams can benefit from a lack of player safety in contract negotiations. Source.
  • You shouldn’t try to maximize your score in Words with Friends/Scrabble. Source.
  • In speed sailing, competitors deliberately choose paths they believe will be slower. Source.
  • The first player wins in Connect Four. Checkers ends in a draw. Source.
  • Chess has a solution, though we don’t know it yet. Source. (Or maybe not.)
  • Warren Buffett was never going to pay $1 billion the winner of the March Madness bracket challenge. Source.
  • Park Place is worthless in McDonald’s Monopoly. Source.
  • Losing pays. Source.
  • As drug tests become more accurate, they should be implemented less often. Source.

Am I missing anything?

26 responses to “Game Theory Is Really Counterintuitive

  1. Pingback: A List of Game Theory Results that Are Odd, Cool, or Counterintuitive (x-post /r/gametheory) « Economics Info

  2. In your “Chess has a solution” point, you refer to Zermelo’s theorem, which is about finite games.

    However, chess is not a finite game (although many people think it is because they mis-interpret the rules).

    See http://chess-musings.blogspot.nl/2012/04/chess-is-infinite-game.html for an example of a position where rational play by both sides means a game will go on forever.

  3. Pingback: A List of Game Theory Results that Are Odd, Cool, or Counterintuitive (x-post /r/gametheory) | Amateur-Science

  4. Thanks, Will. I see several things here that I can use in the courses I teach.

  5. Sometimes having less power is better than having more power. (See the Chair’s Paradox, although I don’t have a good non-textbook link at the moment.)

  6. Consumers are better off with biased media firms rather than unbiased ones: http://chenv.bol.ucla.edu/ChenV_Bias.pdf

    • Excellent.

      • Just a quick follow up, but the description you had inserted isn’t quite right. It isn’t that biased media is better, but rather more media / data is sourced because firms have a bias. It’s pretty interesting if you take a look at the model.

  7. “Every Voting System is Manipulable” is an exaggeration of the implications of strategic voting. Yes, the Gibbard–Satterthwaite theorem proves that a dishonest vote could profitably exist in any system, however there are already systems where intentionally doing so requires the voter to:
    1) Have perfect (or near-perfect) information about exactly how everyone else is voting, and
    2) Solve an NP-hard math problem.

    When breaking the vote requires more knowledge than any politician has, and more computing power than breaking the cryptography of all the world’s banks, I’d say it’s not particularly manipulable.

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  10. William, I would be interested in your strategy for a real-life one-shot game of Centipede like described in your textbooks. Because you do not know the preferences of the other player and may have difficulty quantifying your own, only the dollar amounts are known – not the payoffs. You might even argue that calling the game Centipede could be wrong because the payoffs are not known – but let’s call it Centipede for now. How would you play?

  11. “Am I missing anything?”
    Yes: Long term, attractive women will be happiest with bearded men who wear flannel shirts. This never fails.

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