A counter-blast to game theory

January 14, 2010

I recently purchased Value Investing by Montier. It’s an interesting book, but it seems to focus more on behavioral finance issues and value investing philosophy than actual techniques. Now, of course, no one describes their investing style as “behavioral finance,” but to a large degree every investment philosophy depends on exploiting some mistake that most investors make so although it’s not all you need to understand to invest, it is something you need to understand. Since the techniques of value investing were invented decades ago and have not really changed much, the book’s focus is fine. It never hurts for value investors to read a well-written book that allows us to renew our smugness; we feel comforted knowing that the great titans of Wall Street are still capable of being outmatched by a little guy who’s capable of remembering that 2+2=4 (but sometimes you can buy it for 3 anyway).

Actually, as to that example, in his multi-part debunking of the efficient market hypothesis he even goes after the well-known statistic that mutual funds generally do not beat the market over long periods. First of all, he explains that mutual funds fail to beat the target index because most of the time they purchase the target index for most of their portfolio to avoid lagging behind. In fact, one bold and daring mutual fund manager was apparently forced by his company to dilute his good ideas with a premade portfolio to better replicate the index. The author’s own study revealed that over a period where good mutual funds earned 12% a year, which was the index average, if you instead considered the managers’ best ideas, as estimated by their largest positions, they managed to pull off 19% a year over the same period. So, the much touted inability of fund managers to beat the market is the fault of the fund management business, not the inability of the parties involved.

John Nash, founder of game theory

He also describes a nifty game that was played at a conference he attended. All the parties guess a number from 0 to 100, and the winner is the one who guesses the number that is 2/3 of the average of the guesses. He describes first that since the winning answer can never be above 67, and that only applies if everyone else guesses 100, he was kind of surprised that there were answers above 67.

There was a small cluster of answers at 50, which he calls “0-level thinking.” So, an answer around 33 would be “1-level thinking” because it assumes that the average guess would be 50, and so 22 I guess would be “2-level thinking.” There was a large cluster of answers around 0 and 1 (perhaps owing to some confusion about whether 0 was a legal answer), and the author noted “these would be the game theorists and the quants.” He is correct that the answer of 0 is “n-level thinking” where n is a decently large number, because if everyone thinks the situation out and pursues optimum strategy 0 is the correct answer. But the actual answer was 17 because the average was 26 (and he concludes that the average professional investor employs 1.6 level thinking, since 50 * (2/3)^1.6 is 26).

But I want to focus on the people who voted higher than 67. He thought it was owing to some confusion about how the game worked, but I think it was just some people who wanted to annoy the game theorists and their fancy book-larnin’. Since only 3 people got the right answer (out of 1000 players and with only 68 “real” answers available, so they actually did worse than a random guess), it is possible that people played to enjoy the game rather than to win. My friend Mike adopts a similar approach to the game of Fluxx; instead of playing to win he tries to play so that the game will last forever, which is not difficult. I think that the people who voted above 67 were just trying to block the game theorists and their optimum strategizing.

I know I would.

2 Responses to “A counter-blast to game theory”

  1. Just to set the record straight:

    I don’t play fluxx to stalemate, but I do QQ when others take that approach. I often play to terminate the game as quickly as possible 🙂

  2. The only time we played it I believe you did play to stretch it out, actually.

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