God is Not Dead

This is a thought that just occurred to me, so I'm going to make this one quick and pretentious; I suspect my reach is exceeding my grasp, but let's give it a try anyway.

A few days ago, Jon Stewart interviewed Jim Cramer and took him to task for his, and CNBC's, failure to see the financial crisis coming; more specifically, for their continued insistence that everything was just fine when in fact, obviously, things weren't. While CNBC clearly completely failed to correctly read the economy, I don't understand why anyone would expect them to, when the investment bankers who actually had billions of dollars riding on the economy couldn't see it coming, either. I mean, seriously; if the chairmen of Bear Stearns, Lehman Brothers, AIG, et al, couldn't foresee their future bankruptcy, how could a cable channel with considerably less interest in the banks' continued health see it coming?

The truth is that no one could see it coming, and this is what people find so hard to accept. So much of life is random and unpredictable, and yet we continually insist on trying to put a framework and predictability onto it. And, so, I would say that Nietzsche was wrong when he said, "God is dead." When he said that, he meant that humans are no longer able to believe in some grand cosmic order, or overarching structure, and are doomed to resort to relativism and nihilism (Wikipedia has a good summary). However, to me, it appears the opposite is true. Humans instinctively believe there is an overarching order; when a financial crisis strikes, it seems impossible that it could not have been foreseen, and if anyone didn't predict, it must be due to their ineptitude, not to any inherent unpredictability. People are frightened by the idea of a true chaotic randomness, and continually resist it. Until they accept it, God will never die.

Rock, Paper, Scissors, and Game Theory

Game theory has long been a fascination of mine, and I'm finally getting a chance to take a class on it here at NYU. We recently had a class where we found the mixed-strategy Nash equilibrium for rock, paper, scissors (RPS), and it made me curious about Nash equilibria for other variants of RPS, which are manifold.

First, of course, I'm going to have to explain some these game theory terms that I'm throwing around. The essence of game theory is exploring decision-making when the outcome of your decision is dependent on someone else's decision. When this is in a two-player game, it's often expressed through a payoff matrix, like so:



This is a payoff matrix for RPS. The left column shows the moves for player one, and the top row shows the moves for player two. The payoffs to each player are listed in the cells, with the format [Player 1's payoff, Player 2's payoff], where a 1 represents a win, a -1 represents a loss, and 0 represents a tie.

Now that we have a payoff matrix, we'll want to find an equilibrium. Specifically, we're going to look for a Nash equilibrium. A Nash equilibrium exists where both players are pursuing a strategy such that neither can improve their payoff if the other play continues to pursue the same strategy. It is obvious that there is no "pure strategy" Nash equilibrium for RPS; that is to say, there's no possible equilibrium where each player plays one move all the time. If player 1 always throws scissors and player 2 always throws rock, player 1 can improve his payoff by always throwing paper instead. However, if he does this, then player 2 can improve his payoff by always throwing scissors, and so on.

When a game has no pure strategy Nash equilibrium, we search for a mixed-strategy Nash equilibrium. A mixed strategy is a grouping of pure strategies, with a proportion assigned to each for often it should be played. In the case of RPS, there is a mixed-strategy Nash equilibrium where each player plays each strategy one-third of the time. This is intuitively unsurprising; each move will win, lose, or tie one-third of the time each.

Another variant of RPS is Rock, Paper, Scissors, Lizard, Spock, which, in an effort to reduce ties, expands upon the original RPS ("RPS Classic", I suppose) by adding in lizard, which eats paper and poisons Spock, but is crushed by rock and decapitated by scissors, and Spock, who vaporizes rock and bends scissors, but is poisoned by lizard and disproved by paper (he is fictional, after all). The payoff matrix for rock, paper, scissors, lizard, Spock is as follows:



It is somewhat more interesting than the classic RPS chart, and certainly does cut down on the number of ties (the probability of a tie is reduced from 1/3 [3/9] to 1/5 [5/25]). However, the Nash equilibrium is essentially the same as for the original RPS: both players play each strategy 1/5 of the time. It's the same game, just slightly expanded.

However, there is another five move variant of RPS that actually adds an additional strategic wrinkle: Rock, paper, scissors, fire, water. In this variant, the original rules hold, except fire beats everything except water, and water, in turn, loses to everything except fire. The payoff matrix looks like this:



The game is said to come with the stipulation that fire can only be used once in one's life time, but this is silly, as the Nash equilibrium can be shown to be, actually, each player playing fire one-third of the time, water one-third of the time, and rock, paper, and scissors each one-ninth of the time. The reason for this is that it's really become a balanced game between three actions, where the three actions are fire, water, and RPS. Fire beats RPS, which beats water, which beats fire. Each of these actions should be played one-third of the time, but "playing" RPS properly means playing rock, paper, and scissors each one-third of the time, and 1/3*1/3=1/9.

The reason I bring this up, and have made such a long blog post about such a ridiculous topic, is because I find this result to be interesting, and worth thinking about, because it is counterintuitive. While water would seem to be arguably the least valuable move, because it only defeats one other action while the other four defeat at least two actions, it actually should be played three times as often as rock, paper, or scissors, even though those would seem to do more. It is solely because the one action that water beats, fire, is the most powerful that water is so valuable move. I think there is a useful lesson to be had here when considering counterintuitive value and pricing. Unfortunately, I don't think I know that lesson yet.

Follow-up on Michael Lewis piece post

Here's a great video from one of the Ted conferences about choice and horizontal segmentation and so forth.

There're a lot of directions I could go with this one, but for now I want to focus on something he mentions in the middle: that people don't know what they want, or at least can't accurately describe what they want. This, I think, backs up to some extent my assertion that people might misunderstand the utility of something to themselves, and thus break a pricing mechanism.

The thing about this point is it really cuts to the heart of most political debate: just how responsible are people for their actions? Libertarians believe in people having complete authority to make their own decisions; extremely statist liberals (for lack of a better term) believe in government superseding people's authority to make their own decisions. Ideologically, I fall more in line with the former belief, and, to a great extent, most Americans do as well, even the liberals, but reality does occasionally suggest that perhaps people shouldn't be trusted to make their own decisions as much. I suppose that's why it's debated over.

Again, I do hope to expand more on these thoughts, but that's what I have for now.

Wall Street and calculating utility

Great article here by Michael Lewis (of Moneyball fame, as previously referenced on this blog) about the financial collapse.

The thing I find most interesting about it is how the heart of the matter is that assets were overvalued, and what that says about a market. Wall Street firms were selling assets that were ridiculously overvalued, and acting as though they had value. It is easy to try to blame the firms for inflating the value of their assets, except people were willing to buy these assets. It takes both a buyer and a seller to set a price, and buyers were just as irrationally overvaluing assets.

This is, in a sense, almost frightening, because it suggests a way in which the market system is flawed. It is essential to a properly functioning market that buyers and sellers understand the utility of what they're selling or purchasing; indeed, that's how the price is set. Buyers only pay a price that's equal to or lower than what the good (or asset) is worth to them, and sellers only take a price equal to or higher what it's worth to them, and an equilibrium is found.

However, what if buyers and sellers aren't able to know what a good is worth to them? It's not implausible. When we discuss the myriad calculations that must be done to determine a good's value, it is unreasonable to think that everyone performs those calculations; surely people value and undervalue goods.

That, however, is the key: error in valuing goods should be random. What happened in the run-up to the Wall Street crash is that error in valuing goods was systematic, and all in the overvaluing direction. This sort of systematic error subverts the market.

Hopefully I'll be able to clean up this post and expand upon it, but these are my thoughts for now.

The Pat Burrell signing

I'm a couple of days late on this one, but I was thinking earlier today that the Rays' signing of Pat Burrell for 2 years and $16 million makes the Phillies look even worse for the Raúl Ibáñez signing. The Phillies signed Ibáñez for 3 years and $30 million to replace Burrell, essentially, even though Ibáñez is 4 years older, isn't as good offensively, is even worse defensively (which is saying something), and, apparently, is more expensive than Pat the Bat. It's absolutely incredible how that worked out. The Phillies ended up paying more money and committing to more years for a player that's straight-up inferior. It suggests a few things:

-We've been seeing the effects of the depressed economy on free agent signings, but this seems to suggest that it's worse than people thought it would be even a few months ago when everyone knew it was bad. (Supporting this notion is the fact that the players' union encouraged free agents to turn down arbitration, even though this has come back to hurt several players [Jason Varitek, for one].)

-The Rays got a tremendous deal. I've heard it suggested that Burrell gave them a discount for some reason. I suppose this is possible, and it would somewhat excuse the Phillies for signing Ibáñez, but it's looking more and more like the market for all-hit no-glove guys just isn't there. I mean, even Manny bloody Ramirez can't get signed, let alone guys like Adam Dunn and Bobby Abreu. I wouldn't be terribly surprised if they (Dunn and Abreu) get deals in the same ballpark.

-Perhaps the Phillies' front office has a real problem with Pat Burrell. I haven't really looked into that, but if there is a problem, it's certainly not a widely known one, because it's not the sort of thing that comes up every time he's mentioned. Furthermore, I also haven't heard any suggestions that he's a problem in the clubhouse. Clearly I don't work in the front office of an MLB team, and if I did, maybe I'd think differently, but I think if I were GM and I had a personality problem with a player, if he went out and performed well and didn't cause trouble in the clubhouse I'd keep paying him and try to re-sign him. But maybe there were bigger problems afoot in Philly.

"The Germans make great stuff, y'know"

So über-blogger Joe Posnanski had a piece mentioning infomercials, and of course ended up talking about the Shamwow. One of the things he highlighted is the fact that the Shamwow ad stresses the fact that it's made in Germany, and he wondered why. To wit:

"If it said: 'Made in USA,' OK, I’d get it, we’re trying to play the patriotic card. But what possible good could come out of people knowing that the ShamWow is made in Germany? Are there people out there thinking: 'Well, Germany is known for their shammy-type products. Who could forget the ShamCow, which was only a four inch square but could suck up an entire half-gallon carton of milk. And the ShamPlow. Those Germans are Shammerrific.'"


I think the idea is that it’s not made in China, Taiwan, Korea, Pakistan, etc. People have an idea that stuff made there is somehow inferior, because they don’t understand how exploiting comparative advantage reduces cost, and figure if it’s that much cheaper, there must be something wrong with it. The recent well-known problems with goods coming from China only reinforces this view. Products from Germany don’t have this same stigma because, if anything, they tend to be more expensive (just think about cars: Mercedes, Porsche, etc.).

This, of course, lends some credence to ideas of upward-sloping demand curves: people assume that if something is more expensive, it must be better. Clearly this phenomenon does not often dominate, but I wonder how pervasive it is.

"If it saves just one life, it's worth it."

A few years ago, the town I live in built a stoplight at an intersection where a high school girl had died in a car accident. While they were building it, I drove past there with a friend of mine and his mother. When he commented that there was really no need to build a street light there, his mother said, "If it saves just one life, it's worth it."

Now, it's possible that his mother knew how much it cost to build and maintain a streetlight there, and decided one life would be worth it, but it's far more likely that she meant that any expense is justified if it saves "just one life"; i.e., lives have an infinite value. This, of course, is absurd, because it would imply we should devote all of our resources towards saving lives. This, in turn, becomes even more absurd, because there are various places towards which resources must be directed to save lives (food, shelter, healthcare, etc.), but if lives have an infinite value, it becomes impossible to efficiently determine just how these resources should be allocated towards saving lives. Infinite values do not work well in a market.

In short, it's clear that lives do not have an infinite value, and there must be some finite value we could place on a life. There must be some dollar value that it's not worth spending, even "if it saves just one life". However, as a society we're extremely uncomfortable placing a finite value on a life, and try to treat all lives as having infinite value, even though this is an untenable position. It is, I think, not difficult to see how many political disagreements can and do stem from this dilemma.

Foreign Guitars and Price Discrimination

So, I was thinking about guitars the other day. I got to thinking about how imported guitars are generally perceived as inferior quality compared to guitars made in the USA. Now, as an econ major, I can state quite confidently that there is no reason that a guitar made overseas should necessarily be of worse quality than one made in the US solely by virtue of the fact that it's foreign made.

Now, it may be the case (and I believe it is, in fact, the case) that, on average, foreign made guitars are lower quality than American-made guitars, but this isn't directly because of which side of the American border they're made on. There's nothing inherent about Americans that makes them better at building guitars than Koreans, or Mexicans, or the Vietnamese, etc. I suspect that American guitar makers (luthiers, to use the technical term) tend, on average, to be more skilled at guitar-making than foreign guitar makers, but this isn't because they're American. You could, undoubtedly, find and/or train perfectly talented luthiers in other countries, and they'd be able to produce guitars cheaper, because of the relative abundance of labor* in that country.

*note that the glaring flaw in my analysis here is the assumption that the labor required for building good guitars is either virtually the same as the labor required for building cheap guitars, or that it's different but both kinds of labor are relatively abundant in the other country. More on this later.


So, to try to illustrate my point, consider two guitars: the Fender Standard Stratocaster and the Fender American Standard Stratocaster. They're two variations on the same model, mainly distinguished by the fact that the latter is, unsurprisingly, made in America, instead of Mexico, like the former. The Standard Strat retails for $399.99, and the American Standard for $999.99. Now, there are concrete things, other than the country of manufacture, that make the American Standard Strat a better guitar. It has better pickups, better paint options, a better tremolo system, better hardware, better wiring, etc. However, there is no reason a guitar identical to the American Strat, with all the improved options, couldn't be made in Mexico. And if it were made in Mexico, it would be cheaper. AFAIK, and here's where the above asterisk comes into play, there is nothing about using the improved materials and hardware that requires a different sort of labor. So, in other words, Fender could make a guitar identical to the American Strat but make it in Mexico, and it would only cost, say, $600 as opposed to the $1000 they currently charge. Why don't they do this?

My best guess is price discrimination. Price discrimination is when a firm that faces a downward sloping demand curve tries to get different consumers to pay different prices based on what they're willing to pay. For example, let's say that a firm sells a product, and if they charge $100, they'll be able to sell 50 units of that product, and if they charge $50, they'll be able to sell 200 units of said product. Clearly, if these are the only two prices they can charge, they'll charge $50, because that generates a revenue of $10,000, as opposed to the revenue of $5,000 that charging $100 generates. However, if they charge $50, they're charging every customer that price, and there are 50 customers who were willing to pay $100 per unit (assuming each customer buys one unit) but are now only paying $50 per unit. If the firm could somehow charge these 50 customers the $100 they're willing to pay, they'd generate a revenue of $12,500. However, this is easier said than done, because it requires identifying the customers who are willing to pay more than $50 without actually going right up and asking them, because of course no one is going to come out and say how much they're willing to pay. A variety of firms in a variety of industries have found ways around this.

I suspect Fender is engaging in something similar. They're segregating the market into consumers looking for a low price guitar, and consumers willing to pay more for quality. By producing their highest quality guitars in America, they're charging consumers who want to pay more for quality, and are presumably willing to pay more, an additional surcharge for an American made guitar, while lowering the price on lower quality guitars (by having them made overseas) for consumers who are more concerned with low cost. This, I believe, is the reason that American-made guitars tend to be higher quality; not because Americans do a better job of making guitars, but the nature of the market means it makes sense to produce higher quality guitars in America.

(NB. It is, strictly speaking, inaccurate to refer to this as "price discrimination", because that refers to charging different groups of people different prices for the same product, which clearly Fender isn't doing. However, I feel that the basic idea is similar; at the very least, it made me think of the idea of price discrimination.)