Haim Shapira - Gladiators, Pirates and Games of Trust: How Game Theory, Strategy and Probability Rule Our Lives

Haim Shapira was born in Lithuania in 1962. In 1977 he emigrated to Israel, where he earned a PhD in mathematical genetics for his dissertation on Game Theory and another PhD for his research on the mathematical and philosophical approaches to infinity. He now teaches mathematics, psychology, philosophy and literature. He is an author of seven bestselling books. His stated mission as a writer is not to try to make his readers agree with him, but simply to encourage them to enjoy thinking. One of Israels most popular and soughtafter speakers, he lectures on creativity and strategic thinking, existential philosophy and philosophy in childrens literature, happiness and optimism, nonsense and insanity, imagination and the meaning of meaning, as well as friendship and love. He is also an accomplished pianist and an avid collector of anything beautiful.

FROM THE SAME AUTHOR:

Conversations on Game Theory

Things that Matter

Infinity: The Neverending Story

Ecclesiastes: The Biblical Philosopher

Nocturnal Musings

A Book of Love

Happiness and Other Small Things of Absolute Importance

CONTENTS

INTRODUCTION

This book deals with Game Theory, introducing some important ideas about probabilities and statistics. These three fields of thought constitute the scientific foundation of the way we make decisions in life. Although these topics are quite serious, Ive made a tremendous effort not to be boring and to write a book thats rigorous and amusing. After all, enjoying life is just as important as learning.

And so, in this book we will

Meet the Nobel Prize laureate John F Nash and familiarize ourselves with his celebrated equilibriumLearn the basic ideas of the art of negotiationReview every aspect of the Prisoners Dilemma and learn about the importance of cooperationIntroduce the world champion in strategic thinkingExamine the Stable Marriage Problem and find out how it led to a Nobel PrizeVisit a gladiators ring and apply for a coaching positionBid in a tender at auction and hope to avoid the Winners CurseLearn how statistics bolster liesBecome acquainted with the presence of probabilities in operating theatresDiscover what the game of Chicken had to do with the Cuban missile crisisBuild an airport and divide an inheritanceIssue ultimatums and learn to trustPartake in John Maynard Keyness beauty competition and study its association with stock tradingDiscuss the concept of justice as seen through the eyes of Game TheoryMeet Captain Jack Sparrow and find out how democratic pirates divide their treasuresFind optimal strategies for playing at roulette tables

Chapter 1

THE DINERS DILEMMA

(How to Lose Many Friends Really Fast)

In this chapter well visit a bistro in order to find out what Game Theory is all about and why its so important. Ill also provide many examples of Game Theory in our daily lives.

Imagine the following situation: Tom goes to a bistro, sits down, looks at the menu, and realizes that they serve his favourite dish: Tournedos Rossini. Attributed to the great Italian composer Gioachino Rossini, its made of beef tournedos ( filet mignon ) pan-fried in butter, served on a crouton, and topped with a slice of foie gras , garnished with slices of black truffle, and finished with Madeira demi-glace . In short, it has everything you need to help your heart surgeon make a fine living. Its a very tasty dish indeed, but its very expensive too. Suppose it costs $200. Now Tom must decide: to order or not to order. This may sound very dramatic, Shakespearean even, but not really a hard decision to make. All Tom needs to do is decide whether the pleasure the dish will give him is worth the quoted price. Just remember, $200 means different things to different

people. For a street beggar, its a fortune; but if you were to put $200 into Bill Gatess account, it wouldnt make any kind of difference. In any event, this is a relatively simple decision to make, and has nothing to do with Game Theory.

Why, then, am I telling you this story? How does Game Theory fit here?

This is how. Suppose Tom isnt alone. He goes to the same bistro with nine friends, making a total of 10 around the table, and they all agree not to go Dutch, but to split the bill evenly. Tom then waits politely until everyone has ordered their simple dishes: home fries; a cheese burger; just coffee; a soda; nothing for me, thanks; hot chocolate; and so on. When they are done, Tom is struck by an ingenious idea and drops the bomb: Tournedos Rossini for me, per favore . His decision seems very simple and both economically and strategically sound: he treats himself to Rossinis gourmet opera and pays just over 10 per cent of its advertised price.

Did Tom make the right choice? Was it really such a great idea after all? What do you think will happen next around the table? (Or as mathematicians would ask, What will be the dynamic of the game?)

FOR EVERY ACTION THERES A REACTION

( THE ABRIDGED VERSION OF NEWTONS THIRD LAW )

Knowing Toms friends, I can tell you that his move is a declaration of war. The waiter is called back, and everyone suddenly remembers they are very hungry, particularly for the high end of the menu. Home fries are soon replaced by a slice of Robuchon truffle pie. The cheese burger is cancelled, and a two-pound steak is ordered instead. All of Toms friends suddenly appear to be great connoisseurs and order from the expensive part of the menu. Its an avalanche, an economic disaster, accompanied by several expensive bottles of wine. When the check finally comes and the bill is equally divided, each diner has to pay $410!

Incidentally, scientific studies have shown that when several diners split a bill, or when food is handed out for free, people tend to order more Im sure youre not surprised by that.

Tom realizes hes made a terrible mistake, but is he the only one? Fighting for their pride and attempting to avoid being fooled by Tom in this way, everyone ends up paying much more than theyd initially intended for food they never meant to order. And dont get me started on their caloric intake

Should they have paid much less and let Tom enjoy his dream dish? You decide. In any event, that was the last time this group of friends went out together.

This scene in the restaurant demonstrates the interaction between several decision-makers and is a practical example of issues that Game Theory addresses.

Interactive Decision Theory would perhaps be a more descriptive name for the discipline usually called Game Theory.

Robert Aumann (from Collected Papers )

The Israeli mathematician Professor Robert Aumann received the Nobel Prize in Economics for his pioneering work on Game Theory in 2005. Following his definition, lets pin down Game Theory as a mathematical formalization of interactive decision-making .

Please, dont panic! In this book I shall try to refrain from using numbers and formulae. Many excellent books do that anyway. I will try to present the more amusing sides of this profession and will focus on insights and bottom lines.

Game Theory deals with formalizing the reciprocity between rational players, assuming that each players goal is to maximize his or her benefit, whatever that may be.

Players may be friends, foes, political parties, states or anything that behaves interactively really. One of the problems with game analysis is the fact that, as a player, its very hard to know what would benefit each of the other players. Furthermore, some of us are not even clear about our own goal or what would benefit us.

This is the right place to point out, I guess, that the participants reward is not only measured in money. The reward is the satisfaction players receive from the results of the game, which could be positive (money, fame, clients, more likes on Facebook, pride and so on) or negative (fines, wasted time, ruined property, disillusionment and so on).

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