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Game Theory 101: Of Madness, Mathematics, and Dynamic Indexing

By Jesse Czelusta (from the October 2000 issue of Index Rx)

In 1949, John Nash was a brilliant young graduate student working on a path-breaking thesis entitled Non-Cooperative Games. He was also about to go mad, as an army of imagined voices prepared to haunt him for the next four decades with, as he later described them, "telephone calls in my head, from people opposed to my ideas." Yet despite his tragic mental condition, Nash would go on to create some of the most significant mathematical ideas of his lifetime, and 45 years later would win the Nobel Prize in economics for his 1949 paper. Today, Nash is known by economists as the father of game theory, an area that comprises a substantial portion of current economic research.

One of the most elegant and important concepts that Nash pioneered was a notion of equilibrium so powerful that it can be used to predict the behavior of everyone from politicians, to military strategists, to investors. Simply put, a Nash Equilibrium is a state of the world in which each individual's actions are optimal given the actions that everyone else will take. This idea is part of the foundation for Dynamic Indexing.

To illustrate the notion of a Nash Equilibrium, and to better understand why Index Rx has been so successful, consider a few examples. First, imagine that you are a driver in a small country with lots of cars but no traffic laws. You are free to drive on whichever side of the road you choose, and so is every other driver. Assuming no government intervention, which of the following do you think is more likely to be the outcome of this experiment in mayhem?

Scenario 1: Fifty percent of people drive on the right, fifty percent drive on the left. Your morning commute makes LA look like highway nirvana, as you roll slowly from one head-on collision to the next; or

Scenario 2: Everyone drives on the same side of the road.

Nash thought that scenario 2 would almost certainly be the outcome; this is perhaps the simplest example of a Nash equilibrium. Consider your decision: given that everyone else is driving on the right, which side would you choose? If you said "left," then the cuckoo's nest is for you. It is also not hard to see how this type of equilibrium could occur naturally, with absolutely no cooperation among individuals: as soon as more than fifty percent of drivers chose a side, you would want to choose the same side to minimize the chances of a collision.

Now consider another example. You are an investor deciding how to allocate your savings. You can invest in one of two companies: Tech or Old-Blue. You have inside information, not available to anyone else, that the net present value of Old-Blue is $997 trillion, while Tech will never at any point in the future turn a profit.

Right now, your decision may seem obvious, but consider this: everyone else thinks that Tech is the greatest thing since wide-slotted toasters, with every CNBC guru touting it's praises, and Lou Rukeyser devoting a whole issue to the merits of this wonder company. Further, you know that everyone else will not know the truth for a long time, and will continue to pour their 401K money into Tech's stock.

Now what do you think? Old-Blue is the better company, but given what everyone else is thinking, its stock won't be going anywhere for a very long time. Tech, on the other hand, is a Silicon Valley nightmare, but an investor's dream. People will be bidding up the price of Tech's stock for some time to come. In fact, your calculations tell you that Tech fever will cause the price of the company's stock to rise from its current level of $1 to over $500, which will represent a price-earnings ratio of 9,837. Old-Blue stock, however, will languish at around $1 until people learn the truth.

As you can see, there is only one thing to do: buy Tech until everyone else starts to buy Old-Blue. Notice also that even if every other investor had exactly the same information as you, the outcome would be exactly the same, as long as each individual thinks that every other investor believes in Tech. This outcome is the Nash equilibrium: given that everyone else will buy Tech, you should too, despite the fact that the company is inherently worthless.

The traditional buy and hold investor would have missed an incredible opportunity. Conventional wisdom posits that paying attention to the fundamental profitability of companies is the only way to invest. But Index Rx is unconventional. We know that in investing, the only thing that matters is what everyone else is going to do. Fundamentals are only as important as everyone else thinks they are. Period.

Thus, the insane genius of Index Rx. We have always outperformed the market by keeping our finger on its pulse. Dynamic Indexing is based on the idea that we can't predict the future, that we don't know how profitable a given company or sector will be, but that we do know that there are patterns to investors' behavior that are consistently repeated. All we need to do is what everyone else is does, before most of them do it, however fundamentally crazy that may seem by conventional standards. We will continue to make money by realizing what the experts don't: when the Mad Hatter is running the tea party, the best you can do is to follow the White Rabbit.

 

 

©2007 Index Rx Inc.