iron instrument through his head an inch and a fourth in circumference, and three feet and eight inches in length.

Amazingly, Gage recovered quite nicely from having this enormous metal bar pass through his brain. The bar weighed more than 13 pounds and was actually an inch and a half in diameter (larger than the circumference reported in the paper). Within less than a year of the accident, Gage felt strong enough to return to his railroad job. Furthermore, to a large extent his mental processes seemed intact.

His colleagues, however, soon found that Gage was not himself. He suffered from a number of new negative personality traits, and his coworkers concluded that he was no longer Gage. In particular, Gage lost the ability to execute plans that he made for the future. Even if his mental functions were unimpaired, the fact that his prefrontal cortex was no longer in charge prevented him from returning to his job as foreman and he subsequently left the employ of the railroad.18

The list of human foibles and weaknesses is a long one. Well now look at the most important demonstrations of individual irrationality that apply to investing. Readers who are interested in the topic more broadly are encouraged to read Richard Thalers The Winners Curse, or Nobel Laureate Daniel Kahnemans Heuristics and Biases (edited by Kahneman as well as Thomas Gilovich and Dale Griffin).19

Irrationality #1: Pride Goeth before a Financial Loss

Paul Tudor Jones II is a legendary trader who has made hundreds of millions of dollars. Some of his exploits are covered in Market Wizards.20 My college roommate from the University of Michigan, Peter Borish, worked with Paul. Through Peter, I met the legendary trader and was able to spend some time with him.

You might think that great traders dont suffer from the same biases as the rest of us. That may be true, but my impression is that they are more

effective at limiting the damage caused by self-destructive aspects of human nature. When I visited him, Paul Tudor Jones had two handwritten signs over his desk. I interpreted them as messages designed to help his prefrontal cortex control his lizard brain.

One sign said, Observe that the blade of grass that resists the lawn mower gets cut down, while the blade that bends remains uncut.

In many areas of our lives, the right course requires us to swallow our pride, take a loss, and move on. If we are unwilling to bend, we, like the blade of grass, will suffer.

One of the most-studied areas in behavioral economics documents how peoples stubbornness costs them money. The setting is called the ultimatum game, and it is a very simple negotiation between two people. The game asks them to divide up a lump sum of money through a process that is decidedly unfair. One of the pair, called the Proposer, gets to suggest how the money should be divided. The second, called the Responder, is not allowed to counterpropose, but must accept or reject the ultimatum offer.

I played the ultimatum game in a workshop run by my advisor, Nobel Prize winner Professor Vernon Smith. In the version that I played, I won the right to have the proposal power by scoring well on a trivia question. I now had $100 and the right to set a take-it-or-leave-it offer to another workshop participant. Furthermore, the decision was made in an anonymous manner. Neither my counterpart nor I knew, or would ever learn, each others identity.

So I have $100. I can make an offer to my hidden counterpart that she or he can earn $10, $20, or any multiple of $10. If my offer is accepted, I keep my part of the $100 and my counterpart goes home with whatever cash I have offered. If my offer is rejected, we both earn $0. What to do? Lets assume for a moment that ones goal is to make as much money as possible. (That was my goal in the $100 ultimatum game.)

Heres how I analyzed the game. The responder is in a tough situation. She or he can take whatever I offer or get $0. So even if I offer a small amount, the responder earns more money by taking my offer than by

rejecting the offer. Based on this, I decided to offer $10 to my counterpart, while retaining $90 for myself.

Vernon Smith ran the workshop by having us first play the games for real money, then before we learned of our outcomes, we would study previous research on the topic. As I was thinking of how I would spend my $90 (I was confident that my offer would be accepted), we began learning of study after study where responders said screw you to low offers like mine.

Professor Werner Guth and colleagues performed the first ultimatum study, published in 1982. For stakes of 10 German D-marks (this was before the introduction of the euro), the players exhibited pride or a sense of fairness. In fact, 20% of responders rejected the offers. Furthermore, the average proposal was much nicer than mine. While I had offered a mere 10% of the financial pie, the first ultimatum game proposers offered an average of 30%.21

Since the original study, the basic findings have been replicated in literally hundreds of studies. In study after study, all around the world, people reveal themselves to be proud. They are willing to lose money to retain their self-esteem.22

Initially, many people claimed that the results couldnt be true, and suggested the rejections were artificial because the monetary stakes were so low. Vernon Smith and his colleagues tested this supposition by having U.S. participants play the game for $100. They found no difference between play for $100 and play for $10.23

The ultimatum game has been taken around the world, in order to test the role of culture and to increase the stakes even higher. In countries such as Indonesia, researchers have organized ultimatum games played for several months salary. Even with such high stakes, people are willing to walk away from unfair offers.24 And, in spite of cultural variation, Professor Guths original findings have also been found among nonindustri-alized people who still hunt animals and gather plants for a living.25

Are ultimatum game rejections irrational? Not necessarily, but they definitely cost the participants money. Recall that these games are generally