Consulting by RPM || Free Advice Blog

John Nash’s Contribution to Game Theory

I wrote a pretty long post at Mises Canada trying to give the average person a real sense of what Nash did in his dissertation. Ron Howard is not the hero of my post. An excerpt:

The central result from the work of vNM was the minimax theorem. The full details are here, but the intuition is: In a finite two-person zero-sum game, there is a value V for the game such that one player can guarantee himself a payoff of at least V while the other player can limit his losses to V. The name comes from the fact that each player thinks, “Given what I do, what will the other guy do to maximize his payoff in response? Now, having computed my opponent’s best-response for every strategy I might pick, I want to pick my own strategy to minimize that value.” Since we are dealing with a zero-sum game, each player does best for himself by minimizing the other guy’s payoff.

This was a pretty neat result. However, even though plenty of games–especially the ones we have in mind with the term “game”–are two-person zero-sum, there are many strategic interactions where this is not the case. This is where John Nash came in. He invented a solution concept that would work for the entire class of non-cooperative games–meaning those with n players and where the game could be negative-sum, zero-sum, or positive-sum. Then he showed the broad conditions under which his equilibrium would exist. (In other words, it would not have been as impressive or useful if Nash had defined an equilibrium concept for these games, if it rarely existed for a particular n-person positive-sum game.)

Problems With the Comments?

At least two of you have written me lately, complaining that your comments are being consumed. (And you’re not even referring to Lord Keynes’ criticism.) Can you tell me specifically what you are experiencing, and also for how long? There was a recent maintenance action that WordPress performed, so if something was screwed up today or yesterday, it might be that.

(And yes yes, I am aware of the irony of asking people to post in the comments how they are having trouble posting in the comments.)

Everyone Relax: Largest Hedge Fund Says No Bubble

A CNBC story tells us that Bridgewater Associates–a hedge fund overseeing $169 billion in assets–recently sent a note to clients arguing that the U.S. economy was not in a bubble. The story summarizes the note’s main points:

Factors arguing against a bubble are, according to the authors:

• Prices have increased quickly, but not as fast as other bubbles
• Valuations are still in “normal territory”
• Leverage isn’t a major driving force of prices and overall lending is still “modest”
• There aren’t any significant new investors entering the market
• U.S. retail and foreign investors have “modest” positions
• Corporate stock buybacks are sustainable
• Economic sentiment is “less ebullient” than other bubble periods

In short, Bridgewater doesn’t think the situation today is analogous to the Roaring ’20s, the dotcom boom of the late 1990s or the housing-fueled bubble of the mid-to-late-2000s.

Some of those bullet points are hard to quantify, but the second last one is rather ominous: It’s bad when hedge funds are reassuring people that corporations can keep buying back their stock in order to keep prices from collapsing.

And look again at the first bullet point, which claims that prices haven’t risen as quickly as in other bubbles. Well, here’s the S&P 500:

The rise since mid-2011 is pretty steep, blowing the housing bubble period out of the water, and comparable to the late 1990s’ dot-com run-up. If the U.S. government had implemented all sorts of pro-growth policies since 2009, I might be comfortable with the above chart. But actually the last six years have seen a huge increase in federal debt and a big increase in the federal takeover of health care, to mention just two big whammies. Nobody knows the future, but I think the stock market is clearly in a bubble–with a little help from our friends at the Fed.

Vox Runs a “Climate Denier” Piece

Yes I’m being tongue-in-cheek, but I’m also serious. Look at how David Roberts at Vox describes what these climate scientists are doing. The following are *his* words:

Climate scientists, Geden says, feel pressure to provide the good news. They’re worried that if they don’t, if they come off as “alarmist” or hectoring, they will simply be ignored, boxed out of the debate. And so they construct models showing that it is possible to hit the 2°C target. The message is always, “We’re running out of time; we’ve only got five or 10 years to turn things around, but we can do it if we put our minds to it.”

That was the message in 1990, in 2000, in 2010. How can we still have five or 10 years left? The answer, Geden says, is that scientists are baking increasingly unrealistic assumptions into their models. [David Roberts, bold added.]

Yet More on Utility Theory

Another post at Mises CA:

Someone might choose to go to the gym and lift heavy weights, rather than sit on the couch eating pizza. Thus the lifting of the weights gave more utility, even though it was physically painful and very unpleasant per se. Or, a person might choose martyrdom over renouncing her religious or political views. Again, this embrace of death gives more utility to the martyr, but it doesn’t convey happiness or pleasure in any hedonistic sense.

“The Battle Between Good and Evil” Is a Staged Conflict

When I was much younger, I had this idea that there was a mighty struggle between good and evil. God was (of course) leading the forces of light, while the Devil (aka Satan) was leading the forces of darkness. You would see this epic clash play out in literature and film, with secular works such as Star Wars but even with obviously Christian fiction such as Lord of the Rings and The Chronicles of Narnia.

But it turns out I that I was totally wrong. There were certain key events in the Bible that showed how obviously incorrect my view was, but I just didn’t have the capacity back then to take these passages at face value. Here are some examples:

==> Exodus 9: “11The magicians could not stand before Moses because of the boils, for the boils were on the magicians as well as on all the Egyptians. 12And the LORD hardened Pharaoh’s heart, and he did not listen to them, just as the LORD had spoken to Moses.

      13Then the LORD said to Moses, “Rise up early in the morning and stand before Pharaoh and say to him, ‘Thus says the LORD, the God of the Hebrews, “Let My people go, that they may serve Me.””

==> Job 1: “6One day the angels^a came to present themselves before the Lord, and Satan^b also came with them.7The Lord said to Satan, “Where have you come from?”

Satan answered the Lord, “From roaming throughout the earth, going back and forth on it.”

8Then the Lord said to Satan, “Have you considered my servant Job? There is no one on earth like him; he is blameless and upright, a man who fears God and shuns evil.”

9“Does Job fear God for nothing?” Satan replied. 10“Have you not put a hedge around him and his household and everything he has? You have blessed the work of his hands, so that his flocks and herds are spread throughout the land. 11But now stretch out your hand and strike everything he has, and he will surely curse you to your face.”

12The Lord said to Satan, “Very well, then, everything he has is in your power, but on the man himself do not lay a finger.”

==> Jeremiah 27:6: “Now I will give all your countries into the hands of my servant Nebuchadnezzar king of Babylon; I will make even the wild animals subject to him.”

==> 2 Chronicles 36: “22Now in the first year of Cyrus king of Persia—in order to fulfill the word of the LORD by the mouth of Jeremiah—the LORD stirred up the spirit of Cyrus king of Persia, so that he sent a proclamation throughout his kingdom, and also put it in writing, saying, 23“Thus says Cyrus king of Persia, ‘The LORD, the God of heaven, has given me all the kingdoms of the earth, and He has appointed me to build Him a house in Jerusalem, which is in Judah. Whoever there is among you of all His people, may the LORD his God be with him, and let him go up!’””

==> Isaiah 53: “9His [the Messiah’s] grave was assigned with wicked men,
         Yet He was with a rich man in His death,
         Because He had done no violence,
         Nor was there any deceit in His mouth.

10But the LORD was pleased
         To crush Him, putting Him to grief;
         If He would render Himself as a guilt offering,
         He will see His offspring,
         He will prolong His days,
         And the good pleasure of the LORD will prosper in His hand.”

==> John 12:  “37Even after Jesus had performed so many signs in their presence, they still would not believe in him.38This was to fulfill the word of Isaiah the prophet:

39For this reason they could not believe, because, as Isaiah says elsewhere:

Lord Keynes Strikes Again

One of the better-read thorns in my side is a guy (I assume) calling himself “Lord Keynes.” He is definitely smart, and has read a lot of economics, but he’s slick as glass and at best is Chaotic Neutral. I’m posting this exchange on the main page here because it will clear up some confusion over the utility debate, but also because LK frequently tries to trip up my commenters here with quotes from my own work. This places them in the awkward position of either defending what they thought was the Austrian orthodox position and throwing me under the bus, or of staying quiet and letting LK run victory laps. Usually (but not always) this is grossly unfair on LK’s part. I don’t know how his mind works well enough to speculate on whether that is his intention or not, but regardless, here you go…

==> In this comment, Bala wrote: “Utility is the subjective appraisement of the usefulness of a means towards end satisfaction. Nothing to do with emotions, happiness or satisfaction out there.”

==> LK licked his lips, sensing his prey had made a tragic mistake. He dug up three of my books and wrote:

Better break the sad news to Bob Murphy. Apparently he is such an idiot he thinks this:

“marginal utility: The marginal utility of a good or service is the amount of satisfaction—utility—you get when consuming one unit of it.”
Robert P. Murphy, The Politically Incorrect Guide to Capitalism, p. 18.

“We can say that individuals rank outcomes in terms of happiness, utility, satisfaction, contentment, etc.“
Murphy, Robert P. Study Guide to Man, Economy, and State, p. 6.

“In praxeology, happiness (or utility, or satisfaction) is a purely formal term, defined entirely by the subjective goals of the individual actor.”
Murphy, Robert P., Study Guide to Human Action, p. 2.
————-
Poor old Bob: doesn’t understand basic Austrian concepts.

 

==> OK, so what’s the deal? Is Bala totally wrong? Or is Bala right, and I’m an idiot?

Actually, it comes from using the terms “happiness” etc. in different senses. It’s easy for me to explain the distinction, all I have to do is give you the fuller quotation from my study guide to Man, Economy, and State that LK quoted from in the middle, above. Here is the fuller quote:

All action aims at exchanging a less satisfactory state of affairs for a more satisfactory state. We can say that individuals rank outcomes in terms of happiness, utility, satisfaction, contentment, etc. Regardless of the name, these terms are purely formal, and do not imply hedonism or crude Benthamite utilitarianism.

Value rankings are always ordinal, never cardinal. There is no unit of happiness or utility, and hence we can only say that a man preferred A to B; we never say he preferred A “three times as much.” — Yours Truly, Study Guide to Man, Economy, and State, p. 6

Cardinal vs. Ordinal Utility

Uh oh, it’s David R. Henderson and me vs. Tyler Cowen and David Friedman. How do you rank the gladiators? An excerpt:

There has been a flareup in free-market economist circles over the issue of “interpersonal utility comparisons.” First Tyler Cowen wrote a post that took it for granted that a rich man got less utility from an extra dollar than a poor man did (although Cowen didn’t think that justified government redistribution by itself). In response, David R. Henderson expressed puzzlement that Cowen overlooked the fact that such an interpersonal utility comparison (IUC) was nonsense, because utility is an ordinal concept. Then a bunch of people,including David Friedman, jumped into the fray, claiming that Henderson was outdated because von Neumann and Morgenstern had shown how we could in fact construct cardinal, not ordinal, utility functions.

In the present blog post I’ll hit the key points in this dispute. To cut to the chase, I agree with David R. Henderson: The way economists use the term, “utility” is an ordinal concept, which expresses a subjective ranking, not an objective measurement. Therefore it makes no sense to say Jim gets more or fewer utils than Sally. Furthermore, the work of von Neumann and Morgenstern does not alter this basic fact: Whether we “believe in” cardinal utility has nothing to do with their demonstrations.