Co-Opetition - Adam M. Brandenburger [23]
It’s All in the Cards To see how game theory works, we’ll start with a deceptively simple game. It’s a slow day at Harvard, and Adam and twenty-six of his M.B.A. students are playing a card game. Adam keeps the twenty-six black cards and distributes one red card to each of the students. The dean is feeling generous and agrees to put up $2,600 in prize money. He offers to pay $100 to anyone—either Adam or a student—who turns in a pair of cards, one black and one red.
That’s the game. It’s a free-form negotiation between Adam and the students. The only stipulation is that the students can’t get together and bargain as a group with Adam. They have to bargain on an individual basis. Where would you expect the negotiations to end up?
Imagine that you are one of the students, and Adam offers you $20 for your red card. Would you take it?
We’ve played this game many times—with students, managers, executives, marketers, labor negotiators, and lawyers. People’s first reactions are almost always the same: Adam is in the stronger position. From the students’ perspective, Adam is literally holding all the cards. If they want to make a deal, they have to go to Adam. He has a monopoly on the black cards. Thus, Adam should do extremely well in the bargaining.
Are you ready now to take Adam’s offer of $20?
Not so fast. Your position is more powerful than it may at first appear, so go ahead and turn down Adam’s $20 offer. Perhaps you counter with a demand of $90. Don’t worry if Adam rejects your counteroffer. Sit tight. Even if you and Adam can’t agree on a deal right now, the game’s not over.
Adam negotiates deals with each of the other twenty-five students. What happens next? Adam still has one black card left, and there is still one red card out there. It belongs to you. To make that last deal, Adam needs you just as much as you need Adam. With you and Adam now in completely symmetric positions, neither of you has an edge in this one-on-one bargaining. A 50/50 split is the most likely outcome.
By waiting, you can get $50 for your red card. Since the eventual deal will be 50/50, Adam and you might as well agree to a 50/50 deal up front. And since any student can play your strategy, the outcome is likely to be 50/50 all around. The game really comes down to twenty-six separate bilateral negotiations. To accomplish each deal, Adam needs the student just as much as the student needs Adam.
Barry then decides to try the same game back in New Haven. But as he stands in front of the class, it becomes apparent that Barry is not playing with a full deck: he’s missing three of the black cards. An unfortunate accident, it seems. Barry plays the game with twenty-three black cards and distributes the twenty-six red cards to his students. As before, a black card and a red card together are worth $100. Where will the bargaining between Barry and his students end up? With a smaller pie to go around, will Barry and his students end up worse off than Adam and his students?
Once again, put yourself in the class. Barry offers you $20 for your red card. Would you take it, or would you hold out for more?
If you try your previous bargaining strategy, you’ll be in for a surprise. This time, holding out is a bad idea. Because Adam had twenty-six cards, he needed all twenty-six students in order to make all the matches. If you turned down Adam’s initial offer, you could count on his coming back. But with only twenty-three cards, Barry is playing a game of musical chairs, and three students will be left out. Should you turn down the $20 and counter with $90, Barry might walk away and never come back to you. You’d end up with a red card and no cash.
What holds for you holds for everyone else. Any student who doesn’t agree to Barry’s terms faces the prospect of being left out. So, one at a time, the students give in. Twenty-three “lucky” students get $20 and three end up with nothing. If Barry offers you $20, take it.
Indeed, Barry could