Do you want to play a game?

You’re at your local bar with a friend and the bartender asks both of you if you’d like to play a game. Being amenable, friendly folk, you agree. The bartender explains the game as follows:

“I’m going to give you each a sheet of paper and on this sheet I want you write down either SHAKEN or STIRRED. Do not tell or show the other person what you’re writing down.

“If both of you write down SHAKEN, neither of you gets a drink. If one of you writes down SHAKEN and the other STIRRED, the one who writes SHAKEN will get two drinks of your choosing (you need not drink both at once). But if both of you write down STIRRED, you’ll each get a drink of your choice.

“You’re welcome to discuss strategy with one another but, as I said, do not tell or show what you’re writing down. You have one minute. Go.”

So what strategy do you adopt and what strategy do you try to convince the other person of? Are they one in the same? If no, why not?

If you’ve seen the British show Golden Balls, you might already be familiar with this scenario — here’s an exceptional example to check out if not:

Now, let’s say the bartender, amused by your willingness to play along, offers another game, this time to you, your friend and the other 98 people in the bar. It goes something like this:

“I’m going to give each of you a piece of paper and on this I want you to write the most you’d be willing to pay for a cocktail, from somewhere between $0 and $20.

“The people in the second highest quartile will each win a cocktail. For example, if there are eight guesses: $5, $7, $10, $12, $15, $17, $19 and $20, the people who guessed $15 and $17 would win.

“In the event of a tie, everyone wins. And, as with before, you can openly discuss strategies but you cannot show them what you write down. Go.”

Now what should you do? If you’d like, take a little time and think it out before reading two recommendations below:

1) The “$20 conspiracy”— If you can convince more than 25% of people to pick $20, everyone who picks $20 will win.

Why? Well, if you have 100 people and at least 26 of them pick $20, that twenty-sixth person will be part of the winning, second highest quartile. And because their guess is the same as the other 25 people who chose $20, our rule about ties will allow ALL of those 25 to win as well.

In other words, at least 50% of people will win — wahoo!

2) The “0 hero”— If you convince more than 50% of people to pick $0, then you’ll create a similar effect to #1, where the “0 hero” group will inch their way into the second highest quartile. In this case, at least 75% of people will win (the 50%+ who pick $0 AND the second highest quartile).

Of course, getting 50%+ of people to agree to $0 is significantly trickier.

The neat thing about this little snippet of game theory is that you can add risks/rewards to alter the group behavior.

For example, if you penalize everyone who over-guesses by making them pay the cost of their guess, you’ll have a much rougher time with the “$20 conspiracy” strategy. Or you can have the “reward” be a cash payout, split evenly among all winners and thus encouraging that only a small number of people win.

And yes, if you haven’t figured it out yet, I just held drinking hostage to teach you game theory and there’s nothing you can do about it.

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