The Art of Strategy
Avinash Dixit, Barry Nalebuff, 2008
Why did a reality show contestant deliberately lose a challenge and win a million? Why did a children's game bring an auction house a deal worth many millions? Two economics professors use real stories to show how to think backwards, how to see the game through another person's eyes, and how to make moves that others believe.
Who it is for
For people who want to make decisions one step ahead of others: at work, in negotiations, in bargaining and in their own promises. You do not need to know any mathematics.
The key lesson of game theory is to put yourself in the place of the other player.
A number hiding from you
Imagine two professors offer you a game. They have chosen a number from 1 to 100. You have five attempts, and after each miss you are told whether the number is higher or lower. Guess it on the first try and you get a hundred dollars; on the second, eighty; then sixty, forty and twenty. It looks like a puzzle about luck with a bit of arithmetic.
Almost everyone starts in the same way: 50, then 25, 37 and 42. After four misses the numbers left are 43 to 49, and there is one attempt left. The authors note that at this point a beginner is more likely to name 49, while a cleverer player names 48. And since they know this, the professors can choose a number so that they pay out less. A random number does not hide from you. A number chosen by a person does hide, because that person is thinking about you too.
This is how the book by Avinash Dixit of Princeton University and Barry Nalebuff of Yale University begins. They call a game any situation in which your result depends not only on your own move but on the moves of other people. Game theory studies such situations. The authors show it with examples from television, sport, business and politics, almost without formulas, in the hope that the reader will become a better manager, negotiator, athlete, politician or parent.
Ahead of you are a team that wins by counting from the end, a reality show contestant who lost on purpose for a million, schoolgirls who suggested a winning move to an auction house, and a billionaire who devised a promise he will never have to keep. Behind all these stories stands one skill: seeing the whole game, with its future moves and the people who take part in it. We begin with the simplest rule.
Twenty-one flags: start thinking from the end
In one season of the American reality show Survivor, where contestants compete in the wild, two teams faced twenty-one flags. They took turns, and each turn one could take one, two or three flags. Whoever takes the last one wins the challenge. Dixit and Nalebuff analyse this game as a teaching case: the right first move in it can be seen only by looking from the end.
Try reasoning backwards. If your opponent is left with four flags, he has already lost: whatever he takes, one, two or three, you take the rest, including the last. So your aim on every turn is to leave your opponent a number of flags that is a multiple of four: twenty, sixteen, twelve, eight, four. From twenty-one, the first player takes one flag, and then answers each move of the opponent so that together they take exactly four per round. The game is solved before it begins, if you know how to count from the end.
The authors call this the first rule of strategy. It works everywhere that players move in turn and can see what the other has done. Such situations are easy to draw as a game tree: a diagram in which each fork means someone's choice and the branches lead to different endings. You first look at the ends of the branches and work out what the other person will choose there, and only then decide where to step yourself.
The simplest tree in the book is familiar from the Charlie Brown comics. Lucy holds the ball and invites Charlie Brown to run up and kick it, and at the last moment she pulls the ball away, and Charlie falls on his back. If you draw the tree, the answer is obvious: since Lucy chooses at the end, and she always pulls the ball away, Charlie's best move at the very start is to say no. His mistake is not a weak kick, but that he thinks only about his own step.
Hence a practical conclusion. Before an important decision, whether it is a change of job, a reply to a profitable offer or a hard condition in a dispute, ask yourself three questions. How will this end in two or three moves? What will the other person do when their turn comes? And which of your first steps leads to the ending you want?
About the author
Avinash Dixit is a professor of economics at Princeton University. Barry Nalebuff is a professor at the Yale School of Management. Together they wrote another well-known book on strategy, “Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life”.
All books by this author: Avinash Dixit, Barry Nalebuff
Terms from the book
- Cortés
- Ultimatum
- Yale
- Buffett
- pounds
- Luther
- Game theory
- Prisoner's dilemma
- Princeton
- Borneo
- Conner
- strategic move
- Survivor: An American reality show on air since 2000: contestants live in the wild, compete in challenges and are voted out one by one. The Russian version was called Last Hero.
- game tree: A diagram of decisions in which each fork is one participant's choice and the branches lead to possible outcomes. It is used to reason from the end back to the beginning.
- Charlie Brown: The main character of the American comic strip Peanuts by Charles Schulz.
- Lucy: Lucy van Pelt, a character in Peanuts, who again and again pulls the football away from under Charlie Brown's foot.
- idol: In Survivor, a figurine that gives immunity: its holder cannot be voted out in that round.
- jury: In Survivor, the group of contestants eliminated near the end, who vote to choose the winner.
- Hatch: Richard Hatch, the winner of the first season of Survivor in 2000.
- Wiglesworth: Kelly Wiglesworth, a finalist in the first season of Survivor, who lost the jury vote to Richard Hatch.
- Boesch: Rudy Boesch, a contestant in the first season of Survivor, a retired US Navy serviceman.
- Fredo: A character in a teaching example in the book: a man who asks for money for his business. The authors invented the name for the story; it is not a real entrepreneur.
- Hasiyama: Takashi Hasiyama, a Japanese collector and head of the company Maspro Denkoh, who in 2005 left the choice of auction house to a game of rock-paper-scissors.
- impressionist: An artist of the movement that arose in France in the second half of the nineteenth century and sought to convey a living impression, light and movement. Among the impressionists are Monet, Renoir and Degas.
- Christie’s: One of the two largest auction houses in the world, founded in London in 1766.
- Sotheby’s: One of the two largest auction houses in the world, founded in London in 1744, Christie’s main rival.
- America’s Cup: The oldest international trophy in yachting, contested since 1851.
- Liberty: The American yacht that defended the America’s Cup in 1983.
- Australia II: The Australian yacht that won the America’s Cup in 1983.
- ABC: One of the largest television channels in the United States.
- Primetime: A news programme on the ABC channel.
- de Gaulle: Charles de Gaulle, French general and statesman, leader of Free France in the Second World War and President of France from 1959 to 1969.
All terms
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