The All-Seeing Eye

Musings from the central tower…

The Traveler’s Dilemma

Now for some real content. I came across this article in Scientific American about the Traveler’s Dilemma. To explain briefly, the TD is a game in which two players are each asked to select a number within certain boundaries (2 and 100, in the example). If both players select the same number, they are rewarded that number of points. (In the example, each point is worth $1, which makes the game of more than academic interest.) If one player’s number is lower, they are each awarded points equal to the lower number, modified by a reward for the player who selected the lower number and a penalty for the player who selected the higher number. So, for instance, if you choose (48) and I choose (64), you get 50 points and I get 46 points.

The intuition that I had upon reading the rules of this game was that it would be “best” for both players to choose (100). That is certainly true from a utilitarian point of view: (100, 100) results in the highest total number of points being given out – 200. The runners up are (99, 99), (100, 99), and (99, 100) with 198. However, there are two small problems – here’s the dilemma part – that prevent (100, 100) from being the “best” choice: one, the players are not allowed to communicate, and two, the (100, 99) and (99, 100) plays result in one player receiving 101 points – an improvement, for that player, over a 100 point reward.

So, the reasoning goes, if player one predicts that her opponent will play (100), she should play (99) in order to catch the 101 point reward. Her opponent, however, ought to use this same strategy, and also play (99), in which case player one ought to play (98) in order to trump her opponent, and so on and so forth. This reasoning degenerates to a play of the minimum number – in the example, (2). According to Basu, the author of the article, “Virtually all models used by game theorists predict this outcome for TD.”

However, reality does not follow these models. When people are asked to play the TD, many of them choose 100. Many of them choose other high numbers. Some seem to choose at random. Very few choose the “correct” solution – (2) – predicted by game theory. Something’s up.

Basu takes this to mean that all of our assumptions about rational behavior need to be questioned. With my philosophical background, I happen to have different assumptions about rational behavior than the mainstream, and so for me the results of the TD are not surprising in any way. But perhaps the best way to explain why the results to not surprise me is that I am a gambling man. Continue reading

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January 24, 2008 Posted by | Economics, Game Theory | , , , , , , , , , , , | 6 Comments

The System Of The World

Aside from being the final installment in Neal Stephenson‘s excellent Baroque Cycle, The System Of The World is an important part of a metaphor for my approach to matters philosophical. It goes like this:

Picture a system of equations. Or just consider this one:

a + b = 3
2a + b = 4

It’s a very simple system with a very easy solution: a = 1, b = 2. But how does one solve this system? Well, one method is to examine one equation to try to find a relationship that can help us solve another equation. If we consider the first equation, we can discover that b = 3 – a. If we use this insight about b’s value in the second equation, we get the equation 2a + 3 – a = 4, which we can then solve for a. Once we know that a = 1, things become very easy.

So a system of equations can be solved by, essentially, cross-referencing the information in one equation with the information in the others.

This sort of action, however, is not limited to manipulation of numbers. Philosophy, I believe, works the same way. We can analyze one work of philosophy, or literature, or what have you, and use the conclusions we draw to analyze another different work in a different field, and from this cross-referencing we can derive new equations – perhaps ones with easier solutions.

Let’s work on a very prominent and easy example: The Oedipus complex. Freud looked at a dramatic and mythological character, Oedipus, and from his story drew some conclusions about human nature, which he then applied to the field of psychoanalysis to achieve new and unexpected results. We can challenge Freud’s particular assertions, his methods, etc, but we cannot challenge the fact that Freud was incredibly influential and his insights essentially generated a whole new science.

So where do we find insights like Freud’s? Insights that, regardless of their ultimate validity, help us to look at old problems in new ways? Insights that open up entire new fields of enquiry? The answer is, anywhere.

Each philosophy, each story, each insight, represents a piece of information, an equation in the System of the World. Each equation helps us decode other equations, helps us situate other ideas in reference to one another. All that is needed is for us to find relations, but the fun thing is that everything is related. Anything can be a metaphor for anything else, if creativity and thought are put into it. You might even say that every thought and image we have is a metaphor – after all, a picture of a pipe is not a pipe. And now we’re verging into epistemology and cognitive science. How, exactly, are thoughts organized in our minds? How do we form knowledge? Difficult questions, and well beyond the scope of this post. Suffice it to say that time will tell whether my methods are valid – whether the insights I am able to produce contain truth or falsehood.

January 24, 2008 Posted by | About | , , , , , , , , | Leave a comment