The Art of Strategy

The Art of Strategy is the authors' second book on Game Theory. The first was called Thinking Strategically, and was published in nineteen ninety-one. Eighteen years ago, readers were interested in competition, and beating their opponents. This new book has more emphasis on co-operation, and on watching and influencing what others do. The authors say The Art of Strategy has an outlook that is older and wiser.

On the book's cover is a photograph of a stone, a piece of paper, and a pair of metal scissors. This refers to the children's game 'Rock Paper Scissors' – indicating that everyone plays games, whether you're a small child or a successful economist. The authors believe that Game Theory is too important to stay locked in academic publications, and they try hard to make this topic fresh and relevant. They explain formulae and use mathematical tables, but they also refer to popular movies and prime time TV.

The wide range of examples, from global warming to baseball, does a lot to keep our interest. But the theoretical parts and the calculus may challenge readers who don't have a strong background in math or science.

So who should read this book? It will certainly appeal to people who want comprehensive information about Game Theory, and the chance to see how it might work in practical situations. More broadly, anyone who wants to become a better strategist will probably find it useful.

So, listen up if you want to find out why it's difficult to act randomly, what we can do to keep our New Year's resolutions, and how game theory can help you lose weight.

The book is divided into three parts and fourteen chapters. The authors begin by introducing the idea of strategic thinking as an art, and they share some entertaining examples of good and bad strategies. Next, they show the principles of strategic interaction as a science. Again, they include fun examples from everyday life, such as slimming and sports.

From then on, the book introduces a variety of different strategies and games. It ends with specific situations that illustrate how strategies work in practice. Finally, the authors present a series of case studies, so that we can start to apply our new-found knowledge.

Chapter One is called 'Ten Tales of Strategy.' It begins with a game, and quite a lot of teasing. Readers are invited to join in the classic 'Pick a Number' game. The range is from one to one hundred, and we have five choices. After each choice, they'll tell us if the number they picked is higher or lower, so we can narrow down our options. The authors say if we guess correctly on our first attempt, they'll pay us one hundred dollars. Of course, they soon admit they're only joking. But as we read on, we realize that part of the lesson is learning how to assess the motivations of other players.

They congratulate us if we come up with the best strategy, which is selecting the midpoint of the range. But then they tell us why it won't succeed. This is because the authors wanted to pick a number that would be hard to find, and so they anticipated our moves. They tell us the main lesson in game theory is to put ourselves in our opponent's shoes.

But the game hasn't ended. We have one last guess. They guess our guess, and they tease us for falling into their trap.

The next example is called Winning By Losing. It comes from the TV show Survivor, and it emphasizes how important it is to anticipate other people's moves. Then the authors question the idea of a 'hot hand.' This is a term that refers to the success of a sports star who regularly leads a team to victory. The authors show that there are many different ways of interpreting why players win.

One of the most enjoyable 'tales of strategy' in chapter one is called 'thinning strategically.' Overweight people allowed photographs to be taken of them in scant swimwear for a TV show. They signed a release form to allow these photos to be published if they didn't slim down by the appointed time.

The authors explain that this was a game the contestants played against their future selves. The strategy here is called 'cutting off options.'

Chapter One ends with a clever challenge. The authors ask us to select the right answer in a multiple-choice test, without knowing the question! The trick here is to remember the motivation of the person devising the test. They don't want a student to get the right answer for the wrong reason, so wrong answers have to be chosen carefully. It's worth working through this example, as it's a convincing introduction to Game Theory.

Chapter Two is about finding answers through backwards reasoning. We learn that there are two kinds of strategic actions in games. The first is Sequential, when players take turns to make moves. The second is Simultaneous, when you have to act without knowing what the other player is doing at the same time.

In games of sequence, players look ahead to work out how their actions will provoke actions from their counterparts, and how these reactions will affect them. The model used to illustrate this is a tree. This is a mathematical form for when one action branches out into two possible responses, which in turn branch out again.

The authors realize that many people may not like using forms or theorizing, but they say these are valuable starting points for further thought.

At this stage, the theory isn't demanding. Readers are guided through looking forwards, as with the tree model, to reasoning backwards. But backwards reasoning usually only works when there's no uncertainty in a game. Uncertainty can come from irrationality, cultural difference or from extreme complexity – as in the case of chess. Chess is such a complicated game that players have to use different models. First, they reason forwards, then they artfully use their experience to feel what would be the best strategy. And lastly, when there are fewer options, they reason backwards.

The authors observe that not all games are what's known as 'zero-sum.' In other words, they're not just about winners and losers. Others types of games might end in win-win situations, or lose-lose results. We learn that most games involved in business and social interactions combine both conflict and shared interests. For example, competition is often healthy, and can lead to improved results for competing players. And in some cases, it may be strategically beneficial to join forces. The next types of game the authors explore are known as Prisoners' Dilemmas. These are simultaneous move games when both sides are coaxed into doing something against their mutual interest.

Chapter Four is called A Beautiful Equilibrium. This refers to the work of John Nash, the mathematician who won the first Nobel Prize for Game Theory in nineteen ninety-four.

The Nash equilibrium is about finding a focal point. One example the authors give is the game where you're told to meet someone in New York, or any other major city, on a certain day. But you aren't told where to meet, or at what time. What you are told is how to recognize the person when you meet them, and know that they have the same instructions. The authors tell us this game can have great importance in strategic interactions, such as playing the stock market.

The authors give you a chance to review the theories they've presented in the epilog to part one. They offer some simple definitions of what a game is, and a summary of what you've learned so far.

Chapter Five is on 'choice and chance.' It begins in a way that seems reassuringly familiar, by discussing the strategies used on a soccer field – for example, with the penalty kick. Readers who like games of probability and randomness will enjoy this.

It may also interest you to know that there's a Rock Paper Scissors International World Championship. Randomness is clearly a concept that excites a lot of people.

The authors argue that it's hard to act randomly. In the game of heads or tails with a coin, we tend to think that after a successive series of twenty heads, for example, that tails is 'due.' That's why the authors say we need a way of calculating how the coin will fall that's utterly independent of our own psychology. They suggest one way to gage randomness is to look at the number of words in a series of sentences, which could be in their own book, or anywhere. If they're odd, make it heads. If they're even, make it tails.

How is randomness useful as a game strategy? It's mostly used to get the public to comply with a rule at a lower cost – as in random drug testing. If the testing was predictable – always at a certain time, and always applied to every participant – it would be both costly and inefficient. This is because participants guarantee the results they need by complying at the times they're going to be tested. Random testing is cheaper because fewer tests have to be made. And it's more efficient, as participants have to comply all the time to make sure they don't get caught out.

Chapter Six on 'strategic moves' looks at New Year's resolutions. A CNN survey found that only thirty percent of our resolutions last into February. The authors explore strategies that use incentives or shame, bringing us back to the dieting example used earlier. They give the example of the conqueror of New Spain, Hernan Cortes, who burned his soldiers' ships when arriving in Mexico. Cutting off options for the future worked for him. This principle is applied to the example of slimmers. The threat of being shamed in the future worked for the would-be dieters.

Chapter Seven is called 'Making Strategies Credible.' It's on the subject of interaction, and how to influence what others think. The authors give a useful list of eight actions that increase commitment to a strategy. These include agreeing to pay a penalty or fine, or using a reputation – so that you lose status or personal credibility if you don't see it through. Another one is to burn bridges so there's no turning back.

At this stage in the book, you may realize that the authors are talking about mind games, and how our minds and language make sense of our world. They imply that everything is a game, if we want to interpret it that way. Game Theory can help us see how different models might apply to different situations in our lives, and if there are patterns to resolution in these models. The authors say that knowing about these patterns might help us think more innovatively about how to act, and gain the outcome we want.

Again, at the end of Part Two, there is an epilog that summarizes key elements of the theories so far.

A brief discussion of what they call 'information manipulation' leads on to Part Three. In chapter eight we learn about the devices used to manipulate information – in essence, controlling how our actions are interpreted. 'Signaling' means revealing information. 'Signal-jamming' means avoiding giving ourselves away, or hiding information. And 'screening' means obtaining information.

The chapter begins with a woman's ploy to check out whether a man she's dating is truly ready for long-term commitment. Then there's an example of screening, which is helpful and informative. It outlines how insurance companies get potential clients to reveal information about themselves. The discussion becomes more complex when looking at the value of higher education – gaining an MBA – from the point of view of signaling, rather than the knowledge gained by taking the course. For employers, it's the amount of time and money invested in the MBA that shows the seriousness and reliability of a job applicant.

The following four chapters are the hardest to follow, because of the calculus and theory. But chapter thirteen, on incentives, is topical and easier to understand. It juggles with the material of many business manuals, including competition between workers, motivating staff, how hierarchies function in the workplace, and how to reward hard work.

If you've read every chapter of this book, the case studies in chapter fourteen will help you figure out how much you've learned. At the end of the book, the list for further reading is generous and valuable. There's also a section called workouts, to test people's understanding of the theory. This book is thorough and informative, although quite challenging for readers who want just a taster on Game Theory. But the examples are varied and interesting enough for even a casual reader to emerge with some ideas and a basic understanding of the different types of theory.

Those who read with more care and dedication will probably find that the models it sets up do help to clarify their thinking in situations involving strategy. In other words, the book could make you more adventurous and confident in your strategic thinking.

Whether it will affect your daily life, or business acumen, may depend more on whether you're prepared to snap out of old patterns of thinking and try a new approach. Ultimately, it may depend on whether you agree with the premise that life is a game!

The Art of Strategy: A Game Theorist's Guide to Success in Business and Life, by Avinash K. Dixit and Barry J. Nalebuff, is published in paperback by W.W. Norton & Co.

That's the end of this episode of Book Insights.