Two Envelopes

Posted on

I was just trying to refresh my knowledge of Bayesian probability theory (don’t ask) and I came across something I hadn’t seen before, the Two Envelopes Problem. I’m a fan of the classic game theory paradoxes, the most commonly known one being the Prisoner’s Dilemma.

The latter, as trite as it might seem after endless repetition, is still really a cornerstone of game theory, and the usual entree into discussions of how game theory can apply to economics and strategic financial decisions. For myself at least it was the first introduction to Nash Equillibrium, a state where no player can unilaterally benefit by changing strategy.

What’s so eye opening when you dive into Nash Equilibrium after a heavy indoctrination in efficient markets theory is the realization that a perfectly understandable system with clear rules, where each player is acting perfectly rationally, can produce an outcome that’s decidedly sub-optimal. It’s a dilemma indeed, which is why cops have been using it for centuries. No matter what strategy the prisoner chooses it’s nearly always optimal to confess, though clearly the optimal strategy for both prisoners is to keep their mouth shut.

Thoughtful and prudent market players acting rationally don’t always produce efficient (or Pareto-Optimal, to use the jargon) results. Interesting. We’ll have to get back to that one.

But back to the envelopes. To summarize, assume an actor is given two identical envelopes, each of them containing a sum of money. One envelope has twice as much as the other. The player selects one envelope and keeps whatever is in it, but as soon as they choose, and before they open the envelope, they are offered the option of switching.

Should they take the offer?

If the envelope in your hand has X amount of money, then the other envelope has either .5X or 2X, with a probability of one half. Now as any self-respecting gambler can, you should run an expected value calculation and thus determine that the value of switching will pay off at .5X half the time and 2X the other half, for an expected value of the switch that works out to 1.25X.

So switching, on average will yield a 25% better return than not switching. Of course once you’ve switched, and you have the other envelope in your hand, you start the problem over from the beginning. And now it makes sense to switch again, for exactly the same reason. And again, and again, and again.

Using math, we’ve proven that switching to the other envelope is always the better choice, no matter which envelope is in your hand. Sounds like the statistician’s version of proving that the grass is always greener.

If you’re waiting for the punch line, there isn’t one. That’s why it’s called a problem.

Scarcity as the new paradigm

Posted on

I was trading emails with a very smart friend of mine recently who had this to say:

There is no stopping the growing price of oil over the long haul, and there are no realistic
alternatives to an oil-based economy. As a result, in my opinion, currencies over the next 10-25 years will
largely be pegged to the value of oil, their dependency on oil / supply of oil, and the resulting health of their economy. Using this as one of many lenses to evaluate opportunities, the US economy is fucked. We
have people that commute 80 miles to work in a car.

It’s a point of view you’re hearing more and more of these days. But I don’t agree.

In the short term there is extremely low price elasticity for oil demand. In other words a modest increase in demand causes massive swings in price. It’s this dynamic that has been driving the market recently.

However, the world can and will adjust for oil that is much more scarce. As my friend notes above it will make it impossible for people in the US to drive 2 ton SUV’s 80 miles to work each day. It will also have major effects on global shipping, just in time business models, massive flows of cheap plastic goods
from Asia, and a lot of other things.

But I would strongly disagree that “currencies over the next 10-25 years will be largely pegged to the value of oil.” And I don’t think the U.S. economy is fucked. At least not forever.

The next 1-5 years may be rough. I think it’s correct to say we’ve entered a new era of resource scarcity that’s not just going to end. But over a 5 year period demand elasticity for oil is non-trivial — and over a 25 year period almost anything is possible.

There are substitute goods for oil past the short term. There are ways to massively reduce consumption and divert to alternate forms of energy. For some things like air travel it’s really hard. For things like home heating oil it’s not hard at all.

For auto travel — which fairly or unfairly tends to get most of the attention, as it’s such an integral part of our lives — it’s a medium term shift that requires things like building rail lines, and people changing their habits and where they live.

What bothers me about the gloom and doom set is that I know this can be done in a generation, easily. I know this because we’ve already done it.

We built the interstate highway system almost entirely from 1950-1970, and we can build its replacement just as fast or faster. If we want to. And when the incentives line up, well then we’ll want to.

Let’s put it this way, if we could go from most people living in rural areas, to cities, to suburbs, all in about 100 years, we shouldn’t be shocked if resource incentives cause another round of shifts over a 25 year
period. That’s a long time, it’s more than a generation. It’s worth considering the change in living habits and demographics from 1925 to 1950 for some context.

The United States continues to be an incredible place for innovation. We have real problems that affect competitiveness (health care, infrastructure, and education high among them) but the economic capacity of the US is still astounding.

Betting that the US will cease to be wealthy and relevant isn’t a bet I would take.

I’ll pay you to quit.

Posted on

It’s a story that has been forwarded around a lot this week, but I was struck by an interesting philosophy at Zappos. They offer people $1000 to quit after a month — the idea is that people who aren’t committed will take it, but the people who stay will be serious about working there.

I found it here:

I spend a lot of time visiting with companies and figuring out what ideas
they represent and what lessons we can learn from them. I usually leave
these visits underwhelmed. There are plenty of companies with a hot product,
a hip style, or a fast-rising stock price that are, essentially, one-trick
ponies‹they deliver great short-term results, but they don¹t stand for
anything big or important for the long term.

Every so often, though, I spend time with a company that is so original in
its strategy, so determined in its execution, and so transparent in its
thinking, that it makes my head spin.

My two cents.

Posted on

Some random thoughts on a Sunday evening, following an interesting discussion I just had. The premise was that the U.S. today looks like Japan in the early 1990’s, and that within the next five years the U.S. will be the #3 economy in the world, and just barely maintaining parity with India at #4.

This sentence I think sums up the argument.

The problem is that America has less and less fundamental value to offer the global economy, and this is getting worse, not better.

Let’s unpack this idea a little bit.

The United States is the #1 country for GDP in the world with a rough number of $14 trillion.

Next up is China at about $7-10 trillion, followed by Japan at around $4 trillion.

India is number four at around $3 trillion GDP.

As a sidebar – this brings up the question of how to count the EU. You can make an argument that it should be compared as a whole to the U.S. economy, though I don’t share that point of view — for example it seems like similar logic could argue for including Canada in the U.S. figure based on close economic ties and border policies, even if the common monetary policy of the EU is the strongest argument.

Either way, the entire EU comes in at about $14-15 trillion, just a hair higher than the US.

And let’s face it, the EU is not a country.

So for India to catch up to the U.S. we’d have to be looking at a five year trend that involves either India growing at an annualized rate of 50% or more a year and/or the U.S. declining at an annualized rate of 50% a year or more.

For reference the worst year of the great depression, 1932, saw a negative growth in GDP of about 13% annualized. And also for reference after 10+ years of stagnation Japan is still wealthy and the third largest GDP country in the world despite its tiny size.

In fairness China is much closer behind, but again, their staggering rate of growth (and it is remarkable, and hard to see as sustainable) is still in the 11-12% annual range. Even starting with an extreme premise it’s very hard to see how the current rankings will change in the near term.

But as of today we have heavy, major problems in debt markets, currency markets, job market, and commodities markets, and various other lurking mayhem in the US economy.

It’s also true that the economy has been spectacularily mismanaged for 7 years now. One could argue that any looming recession is a byproduct of spending several trillion dollars in national resources on a war that has led to higher gas prices and even more “crowding out” effects in debt markets. Also relevant is a regulatory policy infested with moral hazard issues, and a fiscal policy that seem guaranteed to put pressure on the currency and price level. I could go on.

But business cycle contractions are normal. One thing that’s normal about them is every time they happen people go nuts like it’s the first time it has ever happened. Much like people thought somehow the rules of real estate had been revoked when they decided to flip houses.

The rules always apply on the way up. But also on the way down. The media tends to gravitate towards the apocalyptic changing of civilization paradigm shifts, but much like it was smart thinking to be bullish but cautious during the bubble, it’s equally rash to over react now on the bear side. Same as it ever was.

A new administration, some unraveling of the insanity in securitized debt markets, and it might just start to feel good around here again. In the 1930’s people starved, in the streets. Banks failed and wiped out entire communities.

We’re still around. It’s fun to play mental Mad Max but it’s more fun to be an optimist. With every panic lies opportunity.