Thoughts on Game Theory: Part I

I apologize for the time between my articles. Some of the delays have been due to me being on the road. Others have been caused by Card Player having too much content to squeeze it all into one issue. Early in the year I started a series on goals, but so much time has passed since we started setting goals for the new year, that I should definitely move on.

My next thought was to do a column or two on planning for the World Series of Poker. I have done this in the past, and my thoughts on how to prepare and what to do haven’t changed. These old articles are available in the Card Player archives or elsewhere online for those who are interested.

I frequently get questions about game theory, so I thought it would be an appropriate topic to cover. First, let’s start with a definition of Game Theory, and then follow up with a brief history of its development. Then we can examine how and when it should be applied to poker situations.

Game Theory can be looked at as a group of mathematical tools and techniques for analyzing decision making in competitive and cooperative situations in which the outcomes of the participants depend on not only their decisions, but also those of others.

It was originally applied to economic decision making, but has since been used to analyze decisions in a wide variety of contexts, including war, biology, political science, computer science, business, and even social situations such as dating.

Modern game theory is the brain child of John von Neumann, a brilliant mathematician, who wrote papers on the topic and then collaborated with Oskar Morgenstern on the book Theory of Games and Economic Behavior in the 1940’s.

Two interesting bits of trivia: 1) von Neumann was a practical joker, and once drove his friend and fellow Princeton genius, Albert Einstein, to the train station and watched as Albert, thinking of more weighty matters, boarded the train heading away from his destination, New York City. 2) In his later years, Morgenstern taught at NYU. I took his course in Game Theory there in the 1970’s, although in reality graduate students did all of the teaching.

Since the publication of that book, many others have advanced the study of games and applied game theory to a variety of situations. Perhaps the most famous Game Theorist was John Nash, made famous by the book and movie A Beautiful Mind. At some point in this series I will discuss his contributions relating to what has become known as a Nash Equilibrium. I will try to avoid discussions that become too mathematical and focus on models (simplifications of real-life situations) that can be analyzed fairly easily. Most models use numerical values to represent people’s preferences. They also assume that people are rational. Not only are they rational, but they know everyone else is rational, and they know that everyone knows everyone is rational, etc. In recent years, however, behavioral economics has challenged this assumption.

Since I have written a lot without mentioning poker, I will discuss a poker situation that challenges the assumption of rationality. A rational player will be happier if he wins $1,000 than if he wins $500 over five hours of play. But in reality, a player who was ahead $10,000, and then ended up winning only a thousand, will be not be happy. Or at least he will not be as happy as someone who was losing $10,000, and made a great comeback to win $500. This may not be strictly rational, but it is virtually always true in the real world.

I will end part one of this series on Game Theory by presenting a problem suggested by Richard Thaler. A group of people is offered a meaningful prize for the most accurate answer. Every member of the group is told to select a number from 0 to 100 that accurately predicts two-thirds of the average number selected by the group. Think about what number you would choose and why you would choose it. Does the belief that everyone in the group is rational effect your choice? I will discuss answers and the reasons behind them in the next column. ♠

Steve ‘Zee’ Zolotow, aka The Bald Eagle, is a successful gamesplayer. He has been a full-time gambler for over 35 years. With two WSOP bracelets and few million in tournament cashes, he is easing into retirement. He currently devotes most of his time to poker. He can be found at some major tournaments and playing in cash games in Vegas. When escaping from poker, he hangs out in his bars on Avenue A in New York City -The Library near Houston and Doc Holliday’s on 9th St. are his favorites.