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How much can you hope to get in a game? As we'll see, the answer doesn't depend just on the size of the pie to be divided, or notions of fairness. Nor does it depend just on how well you play. What you get depends on your power in the game as well as on the power of others who have competing claims on the pie.

Power—yours and others'—is determined by the structure of the game. Game theory shows how to quantify this power.

Game theory began as a branch of applied mathematics. It could be called the science of strategy. It analyzes situations in which people's fortunes are interdependent. Game theory provides a systematic way to develop strategies when one person's fate depends on what other people do.

Game threory sounds tailor-made for the world of business strategy. But historically, there's been an obstacle preventing the world of business from embracing game theory. The problem is that academics and businesspeople speak two different languages: equations versus experience. Many businesspeople have heard of game theory and suspect that it's a potentially powerful tool. But all the mathematics can be baffling and stops people from connecting the theory to practice. At the same time, game theorists are often unfamiliar with business practice, and some of their theories don't capture reality. Our experiences in teaching, research, and consulting suggest that communication between the worlds of game theory and business practice is both possible and valuable. This book brings theory and practice together.

In this chapter, we explain the fundamental ideas of game theory. In the rest of the book,we'll focus on the application of game theory to business strategy. Here, we're laying the foundations, trying to develop a new way of thinking. To do that, we use some deliberately simple and stylized games designed to illustrate the basic concepts of game theory. We've left out the mathematics, but the reasoning still requires close attention. If you, the reader, invest some time in this chapter, we promise you a big payoff in the chapters that follow, in which we apply these concepts to analyze and develop a wide variety of business strategies.

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?

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 even propose a 90/10 split. There are three students who face the prospect of ending up with nothing. They'd be happy to undercut those who hold out for $20. Anyone who ends up with $10 is still lucky. For Barry, 90 percent of $2,300 is a lot better than half of $2,600.

Losing three cards was no accident. Barry was a little Machiavellian. True, he made the pie a little smaller, but he understood very well how losing three cards would change the division of the pie. He knew that getting a sufficiently large slice would more than compensate for the reduction in the size of the pie.

Just a card game? No, a strategy employed by video game giant Nintendo, which, it just so happens, was originally a manufacturer of playing cards. In 1988-89 there was a shortage of Nintendo's video game cartridges. Nintendo chose to play Barry's version of the Card Game rather than Adam's, but with one big difference—it made a lot more money than either Adam or Barry. More on the story of Nintendo in the Added Values chapter.

Sacking the Cities The National Football League (NFL) scores big by playing Barry's version of the Card Game. By deliberately restricting the number of teams in the league, the NFL ensures that there are always more cities wanting football teams than there are teams. In 1988 the St. Louis Cardinals moved to Phoenix, leaving St. Louis with a football stadium but no team. In its bid to attract a replacements, St. Louis made several overtures to teams. It didn't have much success; all it accomplished was to force cities with teams to match its generous offers. Finally, in 1995, St. Louis persuaded the Rams to move from Anaheim to St. Louis. Now Los Angeles has two empty stadiums, having previously lost the Raiders to Oakland. When the Baltimore Colts bucked Maryland and moved to Indianapolis, that left Baltimore eager to find a replacement. It took a new, publicly financed $200 million stadium and a $75-million up-front payment before the Cleveland Browns decided to make the greener pastures of Baltimore their new home. Where does that leave Cleveland? With an empty stadium.

More and more teams are now acting as free agents. With the lure of a $300-million state-of-the-art stadium and a $28-million relocation fee, the Houston Oilers want to move to Nashville. Then Houston will have— guess what—an empty stadium. Meanwhile, the Chicago Bears are thinking of moving to Gary, Indiana. The Tampa Bay Buccaneers may take a hike to Orlando. The Seattle Seahawks are considering flying the coop, as are the Phoenix Cardinals, yet again.

There are many cities chasing after not-so-many teams. That's why the teams do such a remarkably good job of negotiating stadium deals with municipalities. The teams have all the power; cities that want teams have comparatively little. As a result, even cities with teams don't see most of the benefits. A 1992 estimate put state and local government subsidies to team owners at $500 million annually. And that was when the competition for teams was only just beginning.

By playing Barry's version of the Card Game, the NFL has made money, but at a cost. As teams become less loyal to their hometowns, fans become less loyal to their teams. In the long run, that's bad for the NFL. We'll talk more about the pros and cons of undersupplying the market in the Added Values chapter.

The Card Game is a good story to bear in mind whenever you're trying to understand who has power in a game. We'll refer back to it several times in the chapters that follow.