## Friday, November 03, 2006

### Zero-sum Games and their Non-applicability in Economics

What is a zero-sum game? Well, first perhaps I should explain the meaning of the term "game" here. A game, in this context, actually has quite a specific meaning, a mathematical one. A game in this sense is a situation in which the players have conflicting interests. You can represent a game with an array of numbers which in turn represent choices the players can make, along with the payoffs or expected results. One of the most famous games is the prisoner dilemma, which goes like this:

Bob and Mike are in prison and cannot communicate with each other. They each receive an offer: if you rat on the other guy, you can go free. The catch is that if both prisoners rat on each other, neither goes free and both receive a harsher sentence. If neither rats on the other, then both receive a light sentence. Here's a quote from MathWorld on the subject (names changed to reflect my names):

A dilemma arises in deciding the best course of action in the absence of knowledge of the other prisoner's decision. Each prisoner's best strategy would appear to be to turn the other in (since if Bob makes the worst-case assumption that Mike will turn him in, then Mike will walk free and Bob will be stuck in jail if he remains silent). However, if the prisoners turn each other in, they obtain the worst possible outcome for both.

Interestingly, John Nash's (of the movie A Beautiful Mind) great and original contribution to the subject was to explain that, for example in the prisoner's dilemma, a better outcome could be had by use of cooperation. It's a bit more technical than that, but that's the basic idea. Also, for your information, a Nash equilibrium (which used to be called simply an equilibrium) is a strategy for a game which is perceived to bring the best possible outcome for all players. In the prisoner's dilemma, there are two Nash equilibria: both rat on each other, or neither rats on the other. The latter, however, presupposes pretty much that the prisoners actually can communicate with each other, contrary to the original set-up of the game. But that's ok: we dreamed the game up in the first place, so we're allowed to change the rules.

So that's a game. What's a zero-sum game? A zero-sum game is a game in which if one person wins, the other person(s) loses in an equal amount. To quantify it in terms of money, if Bob wins \$5, then Mike loses \$5: the exact amount Bob wins is the exact amount Mike loses. Therefore, the total amount of money available to either Bob or Mike or both is a constant (a zero-sum game).

So where am I going with this? I want to argue that zero-sum games are, in general, not applicable to economics. Many people simply assume that, for example, if the rich get richer, it must automatically be at the expense of the poor. That would be true if economics were a zero-sum game. I argue, though, as would Austrian economists (see my post below), that economics is not a zero-sum game. Here is the refutation. We assume the law of human action: human beings will always do what they perceive to be for their greatest good.

Value, or wealth, is assigned to goods and services by people. The goods and services would have no value whatsoever if people did not value them. So value is determined by people, not wholly by anything intrinsic in the thing itself. True, what a person can do with the good or service usually influences how the person values the good or service. But a different person might just as easily have a different value on the good or service, because his goals may be different. The mistake many modern economic schools of thought make is in not supposing that real people have anything to do with how valuable something is.

Consider a normal trade: Bob has \$5, and Mike offers to wax Bob's car for said amount. Suppose Bob takes up Mike's offer, and Mike performs the job and gets the \$5. What does this say about values? From Bob's point of view, we can see that Bob evidently values having his car waxed more than having the \$5 which he could use for other purposes. Otherwise, according to the law of human action, he would not take up Mike's offer. Similarly, Mike prefers having the \$5 to having the time he could use doing something else, otherwise he would not perform the service.

What do we have at the end? Bob has something greater in his eyes than what he had before, and so does Mike. They both have something better than what they had previously. Since value is determined by individuals, I claim that value has been increased, indeed you could almost say created.

Because value is determined by people, therefore I claim that in every trade, wealth is created. Otherwise the trade would not occur. Evidently, then, the total amount of wealth in the universe is not constant.

It follows from this that it is not necessarily the case that if the rich get richer, the poor get poorer. As I said before, that would be true in a zero-sum game. But I have just proven that we do not operate in a zero-sum game: wealth is constantly created.

Indeed, I would argue that, in a capitalist system, if the rich get richer, the poor get richer. Why is that? Because when the rich get richer, they invest. They do so because that is the way, in a capitalist system, to get even richer. What does investment do? It enables the companies in which the rich have invested to branch out and do more things (entrepreneurs). However, they cannot do more things without more people to do them. Hence they hire more people. Which people? The people who would work for the money they now can offer: poorer people. It may take several layers of such getting richer/investment/hiring sequences before you get to really poor people, but it will happen eventually. This is called "trickle-down economics": if the rich get richer, the poor get richer. Many academicians have poo-pooed such economics, but such academicians tend to rely on the zero-sum game model which I have just refuted.

Why do academicians rely on the zero-sum game model? Perhaps one reason is because it is parallel to the law of the conservation of mass-energy in physics. They would argue that the total amount of "stuff" (Greek "phusis", I believe, though Lane could correct me; this could be translated "physics": physicists study "stuff"!) in the universe is a constant. Therefore, if one person has more of something, someone else must have less. But they leave out the valuation process of real humans. What the academicians say is technically true. However, the new thing someone might have through a trade is worth more to them than what they had previously (otherwise the trade would not have occurred). Hence value is always increasing, even though the total amount of stuff does need to be a constant.

Interestingly, all of what I have related leaves God out of the picture entirely. God is infinite, therefore He can add to His creation anything He desires without diminishing Himself. This is another refutation of the zero-sum game model. The law of the conservation of mass-energy really needs to be qualified by miracles. One such miracle is the feeding of the five thousand (or the four thousand, take your pick). Food was actually created in that miracle out of nothing. Mass was added to the universe.

And here the physical scientists fall so short: they leave God out of the picture entirely. Because many of them do not want a God in their picture, they ignore Him. They will find a messy refutation in the end. As one person put it, "All the world's philosophers and scientists are climbing the hill of knowledge. And when they get to the top, they're going to find a bunch of theologians who've been sitting there for thousands of years."

So do not be intimidated by zero-sum games being thrown at you; such an inaccuracy has been used to foist population control on whole nations, many liberal notions of welfare and such, etc.

In Christ.

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At 11/04/2006 10:56:00 PM ,  Susan said...

Are you using the term "wealth" loosely, to include more than material gain or even more specifically, monetary gain? That seems to follow from the Bob and Mike example. Certainly Bob did not gain monetarily, at the very least, but materially he arguably could have. Certainly he gained in happiness and intrinsic value, which is something standard economics often overlooks.

The problem I noticed with my college economics class was the stress on monetary gain as the only form of wealth. My teacher thought women should work because it upped our GNP. Period. Economics was turned into a cold, hard analysis of cash, with no reference to the people behind the cash. And contrary to the implication of the course, money does not equal happiness or success.

At 11/04/2006 11:30:00 PM ,  Adrian C. Keister said...

Yes, indeed. Wealth is something more than money. It is the sum total of all those things a person values. I completely agree that monetary gain as the sole focus of economics is a mistake: many people value lots of things more than money. I value time more than money, for example. I would much rather have time to do the things I want to do than money to buy the things I want to buy. Your teacher thought women should work solely to increase the GNP? That's ludicrous!! Naturally, the GNP is the only indicator of the health of this nation!!

Actually, Christian principles of economics would include the prudence of saving, something I have not been able to do yet. In any case, economics these days leave out saving completely, and focus on the GNP and the DOW industrial average and such like. It's an incomplete picture of health. Contrary to popular opinion, spend-spend-spend does not equal a healthy economy.

In Christ.

At 11/06/2006 11:20:00 AM ,  Lane Keister said...

The Greek word "phusis" means something more like "the nature of a thing," rather than the thing itself. Of course, this works well in that physics also studies the physical characteristics of things. The Greeks didn't really have a specific word for "things." They could get at that by a demonstrative pronoun "these things." Or, you could put an adjective into the neuter gender plural, and get a description of the things, like "first things," or "last things," or "all things." Good post, by the way.

At 11/06/2006 10:49:00 PM ,  Susan said...

Ah yes, time :). I definitely value that more than money. . . which is why I charge what I consider to be a ridiculous price for tutoring (and it helps that people willingly pay it). There is also intrinsic value, of course. I babysit two mornings a week for 1/4 to 1/5 of the hourly wage I make for tutoring, but because it is such a blessing to the mother (who homeschools her older daughter), it is worth the "lost" time. Charitable work, parenthood, etc. would be other good examples of intrinsic value that trumps both time and money. Since economics is the study of monies, these factors are often lost, or badly put into clever formulas.

And yes, my teacher thought that a higher GNP was good reason for women to be in the workforce, as if that is the only factor *rolls eyes*

Hmm, I hadn't thought before about saving as being left out of economic analyses. Quite true. Not that I make enough to save much anyway :). And have you ever really thought about the Christian principle of saving/investing/reaping and the Christian principle of generous giving, giving a "second cloak," casting our bread upon the waters, etc? That's an interesting set of ideas to reconcile.