Weekend Gaming -- perfecting the imperfect

[disclaimer -- I've only field tested the first of these, so I can't guarantee that all of the variations will play smoothly. On the bright side, there ought to be plenty of room for improvement. As with all discussions of game variants, you should probably assume that countless people have already come up with any idea presented here.]

When the subject of perfect information games comes up, you probably think of chess, checkers, go, possibly Othello/Reversi and, if you're really into board games, something obscure like Agon. When you think of games of imperfect information, the first things that come to mind are probably probably card games like poker or a board game with dice-determined moves like backgammon and, if you're of a nostalgic bent, dominoes.

We can always make a perfect game imperfect by adding a random element or some other form of hidden information. In the chess variant Kriegspiel, you don't know where your opponent's pieces are until you bump into them. The game was originally played with three boards and a referee but the advent of personal computing has greatly simplified the process.

For a less elaborate version of imperfect chess, try adding a die-roll condition to certain moves. For example, if you attempt to capture and roll a four or better, the capture is allowed, if you roll a two or a three, you return the pieces to were they were before the capture (in essence losing a turn) and if you roll a one, you lose the attacking piece. Even a fairly simple variant such as this can raise interesting strategic questions.

But what about going the other way? Can we modify the rules of familiar games of chance so that they become games of perfect information? As far as I can tell the answer is yes, usually by making them games of resource allocation.

I first tried playing around with perfecting games because I'd started playing dominoes with a bluesman friend of mine (which is a bit like playing cards with a man named Doc). In an attempt to level the odds, I suggested playing the game with all the dominoes face up. We would take turns picking the dominoes we wanted until all were selected then would play the game using the regular rules. (We didn't bother with scoring -- whoever went out first won -- but if you want a more traditional system of scoring, you'd probably want to base it on the number of dominoes left in the loser's hand)

I learned two things from this experiment: first, a bluesman can beat you at dominoes no matter how you jigger the rules; and second, dominoes with perfect information plays a great deal like the standard version.

Sadly dominoes is not played as widely as it once was but you can try something similar with dice games like backgammon. Here's one version.

Print the following repeatedly on a sheet of paper:

Each player gets as many sheets as needed. When it's your turn you choose a number, cross it out of the inverted pyramid then move your piece that many spaces. Once you've crossed out a number you can't use it again until you've crossed out all of the other numbers in the pyramid. Obviously this means you'll want to avoid situations like having a large number of pieces two or three spaces from home.

If and when you cross off all of the numbers in one pyramid you start on the next. There's no limit to the number of pyramids you can go through. Other than that the rules are basically the same as those of regular backgammon except for a couple of modifications:

You can't land on the penultimate triangle (you'd need a one to get home and there are no ones in this variant);

If all your possible moves are blocked, you get to cross off two numbers instead of one (this discourages overly defensive play).

I haven't had a chance to field test this one, but it should be playable and serve as at least a starting point (let me know if you come up with something better). The same inverted pyramid sheet should be suitable for other dice based board games like parcheesi and maybe even Monopoly (though I'd have to give that one some thought).

I had meant to close with a perfected variant of poker but working out the rules is taking a bit longer than I expected. Maybe next week.

In the meantime, any ideas, improvement, additions?

A physicist in econ-land

Noah Smith has some fascinating things to about making the transition to economics as a grad student (via Thoma, of course):

At the time I took the course, I didn't yet know enough to have any of these objections. But coming as I did from a physics background, I found several things that annoyed me about the course (besides the fact that I got a B). One was that, in spite of all the mathematical precision of these theories, very few of them offered any way to calculate any economic quantity. In physics, theories are tools for turning quantitative observations into quantitative predictions. In macroeconomics, there was plenty of math, but it seemed to be used primarily as a descriptive tool for explicating ideas about how the world might work. At the end of the course, I realized that if someone asked me to tell them what unemployment would be next month, I would have no idea how to answer them.

As Richard Feynman once said about a theory he didn't like: "I don’t like that they’re not calculating anything. I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation - a fix-up to say, 'Well, it might be true.'"

That was the second problem I had with the course: it didn't discuss how we knew if these theories were right or wrong. We did learn Bob Hall's test of the PIH. That was good. But when it came to all the other theories, empirics were only briefly mentioned, if at all, and never explained in detail. When we learned RBC, we were told that the measure of its success in explaining the data was - get this - that if you tweaked the parameters just right, you could get the theory to produce economic fluctuations of about the same size as the ones we see in real life. When I heard this, I thought "You have got to be kidding me!" Actually, what I thought was a bit more...um...colorful.

Update: Krugman chimes in with some relevant comments here.

"Premature Ecalculation"

Over the past quarter century or so, journalists, particularly television journalists, have gotten very good at finding excuses for covering sensationalistic non-news stories. Thirty or forty years ago Donald Trump's campaign would have merited about as much coverage as Pat Paulsen's. Now the reporters (eyes bleary with crocodile tears) insist that they don't want to provide a national platform for someone who is probably just in it for the publicity to make provably false claims with racist overtones. It's true that freak shows like Trump bring in the ratings and the consequently the ad revenue, but reporters like Meredith Vieira assure us that they're only giving this airtime because the polls show that he's a 'serious candidate.'

As is usually the case with journalistic hypocrisy, the best rebuttal comes from the Daily Show.

Inessential Yglesias -- understanding the elasticity of oil demand

I'm afraid I'm going to have to differ with Joseph on this one. This piece from Matthew Yglesias manages to leave out most of the good stuff from this excellent post by Adam Ozimek.

For example:

However there are important caveats to these estimates that suggest the real current elasticity is higher. First, the evidence has indicated that the response of demand to price changes is asymmetric: price increases cause a larger response to demand than price decreases. This is because price increases are more likely to cause shifts to newer, more energy efficient technologies than price decreases are to undo such shifts. Any estimate of the average price elasicity then will be a downward biased estimate for the likely response to a price increase.

A recent paper by Davis and Killian The Journal of Applied Economics covers some other econometric issues in the literature. For instance, we know price and quantity demanded are jointly determined, which means that there will be a correlation between the price variable and the errors such that single equation or panel data methods, like those used in the reported IMF estimates, will bias estimates towards zero. Some studies attempt to use exogeneous oil shocks as instrumental variables. This approach is used in the appendix to the IMF study. But this requires the assumption that consumers will respond the same to these shocks as to normal real price appreciation. If consumers expect shocks to be more temporary than a demand led increase in price, this is a questionable assumption.

To understand why this is such an important point, we need to step back and discuss why we choose certain analytic approaches in certain situations, specifically why we shouldn't think about elasticity of demand for gasoline the same way we think about it for fruit juice.

[brief warning: I'm a statistician, not an economist, so the terminology here might not be what you'd hear in INTRO TO ECON, but I suspect the underlying concepts will be basically the same.]

Let's discuss demand in terms of decisions. If I go into the grocery store thinking I'd like some orange juice I almost certainly have some threshold price X in mind. If a carton of juice costs more than X, I won't buy orange juice that day.

Assuming I don't have some sort of weird Minute Maid fixation, doing without juice is probably not a big deal. My consumption is determined by a single simple (rather than complex) decision.

[brief warning II: I'm assuming, for the sake of simplicity, that all the grocery stores and gas stations available to me charge roughly the same prices for comparable items.]

By comparison, my consumption of gasoline is determined by a complex set of decisions spread out over a long time and based on anticipated gas prices. Of these decisions, the impact of the one that's analogous to the OJ decision (go to the store and check the price) is trivial next to choosing where do I live, where do I work and what kind of vehicle do I drive.

Even if there is a there happens to be a hurricane or a revolution at the exact time I'm making one of those decisions and gas is at five dollars a gallon, I probably won't bother factoring that in. Trying to estimate the impact of temporary and unpredictable events is a game best left to the specialists.

But let's say that the five dollar price is the result of a recent buck and a half increase in the gas tax and I only see it going north from here. Now five dollars a gallon is starting to look like a floor instead of a ceiling and I am much more more likely to look at MPG and commuting distance when I make my decisions.

Or, in other words, pretty much what Ozimek said.

Essential Yglesias

Matt Yglesias on taxing oil and gas:

One is that while low elasticity implies that a tax is unlikely to be very effective at reducing demand, by the exact same token a low elasticity implies that taxing whatever it is you’re proposing to tax will be a very efficient way of raising revenue. So if you’re the kind of person who believes the government should raise revenue, then there’s really no possible result in the elasticity literature that should make you hesitate to tax gasoline and/or oil.

The other thing is that these elasticity estimates generally imply that the relationship between price and demand is going to be linear, which is almost certainly false. Which is to say that the estimate is only reliable when you’re considering a relatively small policy shift. Nothing wrong with that, there’s just no way to get an empirical estimate about some crazy shift outside the realm of ordinary experience. But it is a real limitation to what this kind of work can tell us.

The second point, that relationships like these are unlikely to be linear is a theme that Mark has been trying to communicate for years and it is nice to see the idea beginning to get traction.

But the first point is a really good one. I like government (not unlimited government, but unlimited ice cream is bad for me too) and I recognize that we need to raise revenue somehow. If the tax on fuel consumption is a way to raise revenue that is a major benefit.

Now it is true that this could adversely impact the transportation options of the less well off. But there are a number of options including means tested fuel tax credits and improved public transportation infrastructure that could be tried. But I think the bottom line is that this tax is like alcohol and cigarette taxes -- we want to discourage an activity and raise revenue for basic services at the same time; while it isn't optimal tax policy (which might address issues like the capital gains tax) it is a major improvement.

Around a quarter of a million reasons to want to keep your job

I started my teaching career in Arkansas, a state known at the time for many ludicrously small school districts. This caused an exceptionally high administrator to teacher ratio. Supporting all these administrators consequently put an additional strain on an already underfunded system.

I had always thought of this as a Southern problem, but this excellent piece by Dana Goldstein has me questioning that assumption:

One of Governor Andrew Cuomo's contentious budget cutting ideas is to consolidate very small school districts. I'm generally a tax-and-spend liberal, but this is a good idea, especially in relatively densely-populated parts of the state. I was reminded why today by the New York Times, which reported on a controversy engulfing the tiny Westchester village of Katonah, NY, not far from where I grew up. Katonah's school board would like to hire a superintendent named Paul Kreutzer, who happens to be the only superintendent in Wisconsin to have publicly supported Gov. Scott Walker's attempt to ban teacher collective bargaining.

Unsurprisingly, hundreds of Katonah teachers, parents, and students are loudly protesting Kreutzer's appointment.

But what really caught my eye was that if he does get the job, the 39-year old Kreutzer is set to earn $245,000 annually to oversee a district of just six schools and 3,800 students. Ninety-three percent of these kids are white, and just 1 percent are non-native English speakers. Approximately 0 percent of Katonah public school children participate in the federal free-and-reduced-price lunch program.

This reminds me of an anecdote I've mentioned here before.

When I first decided to go into teaching I asked a retired superintendent I knew for advice. The first thing he told me was, "Never trust a superintendent; they'll lie to your face." I think he was being just a bit harsh but I understand his position. Administrators live in an intensely political world where the right move can double their incomes and the wrong one can get them demoted or fired. It tends to test character.

Just to be clear, like teachers, most administrators (particularly most principals) are dedicated educators who genuinely care about their students, but they are also, by necessity, expert game-players who know how to work a system. This is simply part of the skill set. An administrator who's bad at politics will probably be a bad administrator.

But if we can't blame administrators for being good at politics, we can certainly blame many education reporters for being bad at journalism. To the extent that this is a story of labor and management, most journalists have unquestioningly swallowed the line of certain managers* that the blame for any problems in the system rested entirely with labor. Every standard of good journalism should have told them to look at both sides of the issue. Every reporter's instinct should have told them to take with a block of salt potentially self-serving claims of a group of media savvy, politically adept people who are trying to protect high but vulnerable salaries and, in some cases, impressive potential careers in politics and the private sector.

* And to be ABSOLUTELY clear, let me make this point explicitly: I am not talking about most administrators. The majority of superintendents and the vast majority of principals are hard-working and intensely focused professionals whose first priority is the interests of their kids. Just like the vast majority of teachers.

Preblog -- Businessmen seldom believe in efficient markets and rational actors

I've got to head off for lunch in a minute, but I wanted to at least throw this out now and address it in more detail later (hence the term 'preblog'). The impetus was this post* which seemed to assume that the market-based approach was more likely to provide real vs. perceived benefits (my wording, not his).

Back in my marketing days when I was building consumer response models and working with the BAs, we would talk about maximizing the perceived to real value ratio -- find a cheap product that looked expensive. Like many, if not most, of our strategies and business plans, this idea was based on assumptions that violated some of the axioms of freshwater economics.

Efficiency and rationality are useful for businesses for lobbying and PR purposes but most people in the private sector don't believe in them. They think can beat the system. That's why they're there.


* nicely rebutted here and here.

Two quotes

No particular connection here, just a couple of passages that seemed worth passing on.

On top of that, Wall Street does have a habit of boiling everything down to a right/wrong duality: if you say that a stock will go down, you’re right if it does, and wrong if it doesn’t. The intelligence of your analysis, or the idea that all these things are probabilistic rather than certain, rarely even gets lip service. This is why you see so much technical analysis on Wall Street: it makes no intellectual sense at all, but it works just as well as — or even better than — fundamentals-based analysis. (Which, admittedly, isn’t saying very much.) And that’s all that matters.

Felix Salmon

All in all I’d rather have been a judge than a miner. And what is more, being a miner, as soon as you are too old and tired and sick and stupid to do the job properly, you have to go. Well, the very opposite applies with the judges.

Peter Cook via Krugman

Subtracted cities -- the art of falling gracefully

A few years ago, I was doing some work for a young company that had developed a reputation as a growth stock. As I became privy to more of the company's long-term plans, I started to wonder about the sustainability of its strategy. The company seemed to be counting on sustaining growth rates that would soon put us over 100% of the market.

I once mentioned this to a colleague who had drank deeply of the Kool-aid. I expected one of two responses: either he would find this troubling or he would point out a flaw in my argument. He did neither. Instead he just shrugged and smiled and assured me that when we reached that point the people who ran the company would simply find a way to "innovate out of the problem."

It's easy to understand the appeal of growth but good planning and management also have to be able to handle plateaus and even declines. This is true for industries like the newspaper business. It's also true for cities.

From Deborah Potter via Richard Green by way of Mark Thoma:

Detroit stands as the ultimate expression of industrial depopulation. The Motor City offers traffic-free streets, burned-out skyscrapers, open-prairie neighborhoods, nesting pheasants, an ornate-trashed former railroad station, vast closed factories, and signs urging "Fists, Not Guns." A third of its 139 square miles lie vacant. In the 2010 census it lost a national-record-setting quarter of the people it had at the millennium: a huge dip not just to its people, but to anxious potential private- and public-sector investors.

Is Detroit an epic outlier, a spectacular aberration or is it a fractured finger pointing at a horrific future for other large shrinking cities? Cleveland lost 17 percent of its population in the census, Birmingham 13 percent, Buffalo 11 percent, and the special case of post-Katrina New Orleans 29 percent. The losses in such places and smaller ones like Braddock, Penn.; Cairo, Ill.; or Flint, Mich., go well beyond population. In every recent decade, houses, businesses, jobs, schools, entire neighborhoods -- and hope -- keep getting removed.

The subtractions have occurred without plan, intention or control of any sort and so pose daunting challenges. In contrast, population growth or stability is much more manageable and politically palatable. Subtraction is haphazard, volatile, unexpected, risky. No American city plan, zoning law or environmental regulation anticipates it. In principle, a city can buy a deserted house, store or factory and return it to use. Yet which use? If the city cannot find or decide on one, how long should the property stay idle before the city razes it? How prevalent must abandonment become before it demands systematic neighborhood or citywide solutions instead of lot-by-lot ones?

Subtracted cities can rely on no standard approaches. Such places have struggled for at least two generations, since the peak of the postwar consumer boom. Thousands of neighborhoods in hundreds of cities have lost their grip on the American dream. As a nation, we have little idea how to respond. The frustratingly slow national economic recovery only makes conditions worse by suggesting that they may become permanent.

Subtracted cities rarely begin even fitful action until perhaps half the population has left. Thus generations can pass between first big loss and substantial action. Usually the local leadership must change before the city's hopes for growth subside to allow the new leadership to work with or around loss instead of directly against it. By then, the tax base, public services, budget troubles, labor forces, morale and spirit have predictably become dismal. To reverse the momentum of the long-established downward spiral requires extraordinary effort. Fatalism is no option: Subtracted cities must try to reclaim control of their destinies. ...

While we're on the subject of economic assumptions...

James Kwak makes some insightful points about allocative efficiency:

I was catching up on some old Planet Money episodes and caught Allen Sanderson of the University of Chicago talking about how to allocate scarce resources. The first day of introductory economics, he says, there are always more students than seats. Say there are forty extra people, and he can only accept ten more into the class. He asks the class: how should the ten slots be allocated? You can easily guess the typical suggestions: by seniority, because seniors won’t be able to take the class later; by merit (e.g., GPA), because better students will contribute more to the class and get more out of it; to the first ten people outside his office at 8 am the next day, since that is a proxy for desire to get in; randomly, since that’s fair; and so on. Someone also invariably suggests auctioning off the slots.

This, Sanderson says, illustrates the core tradeoff of economics: fairness and efficiency. If you auction off the slots, they will go to the people to whom they are worth the most, which is best for the economy as a whole.* If we assume that taking the class will increase your lifetime productivity and therefore your lifetime earnings by some amount, then you should be willing to pay up to the present value of that increase in order to get into the class. An auction therefore ensures that the slots will go to the people whose productivity will go up the most. But of course, this isn’t necessarily fair, especially when you consider that the people who will get the most out of a marginal chunk of education are often the people who have the most already.

...

But I think the picture is still a bit more complicated. Even if we assume for a moment that allocative efficiency is the only thing we care about, it’s far from clear than an auction will give it to us. If people could (a) predict their increased productivity from taking the class, (b) predict their increased lifetime earnings, (c) discount those earnings to the present (which implies knowing the proper discount rate), and (d) borrow up to that amount of money at the risk-free rate, then, yes, everything would work out OK. But this is clearly not the case, since then people would be bidding thousands if not tens of thousands of dollars to get into the class.

Still, you might say that people’s willingness to pay for the class — even if it’s just that one person is willing to pay $60 and another is only willing to pay $5 — is a valid proxy for the value of the class to them. So instead of thinking in terms of lifetime productivity, we’re thinking of the class as a short-term consumption good, and it would provide $60 of utility to one person and $5 of utility to the other. (Note that we’ve given up the idea of maximizing the ultimately economic impact of the class.) But then we have to ask whether money is a valid proxy for utility, and at this point the chain of reasoning breaks down. My willingness to pay for various goods might reflect their relative utility to me, but saying that different people’s willingness to pay for the same good reflects the relative utility of that good to those people is a much greater leap. Most obviously, a rich person will be willing to pay more for some goods than a poor person, even if those goods would provide more utility to the poor person. Assume for example that the rich person has a wool overcoat, the poor person has no overcoat, and the good in question is a cashmere overcoat.

I'm not against the language of the marketplace

I'm against using it where it doesn't apply.

From Rashi Fein, via Paul Krugman:

A new language is infecting the culture of American medicine. It is the language of the marketplace, of the tradesman, and of the cost accountant. It is a language that depersonalizes both patients and physicians and describes medical care as just another commodity. It is a language that is dangerous.

"On Public Funding of Colleges and Towards a General Theory of Public Options"

The U.S. has the best university system in the world. Mike Konczal has some important things to say about the way we fund it.

As a rule, the Centers for Disease Control give better health advice than Gawker

Not much posting this weekend but I did have to take a moment to make the point in the subject line. This might seem too obvious to bother with but the otherwise very smart people at naked capitalism missed it.

The post in question was by Seth Abramovitch:

Hand Sanitizers Will Not Save You From the Coming Plague

The Food and Drug Administration has issued a caveat today, reminding consumers that any hand sanitizer or antiseptic product claiming to be effective against antibiotic-resistant infection is telling you a Bald. Faced. Lie.

No. They're. Not.

This is a complicated issue and our resident expert is otherwise occupied but I think I can lay out the basics. Rubbing alcohol and chlorine bleach both do well against MRSA and other antibiotic-resistant strains. We can get into a discussion of acceptable wording here which is what the FDA was getting at (admittedly in a poorly written statement) and we can talk about side effects, but if the active ingredient of a product is alcohol or bleach then it probably is effective.

How about hand sanitizers specifically? Wikipedia has a good summary (emphasis added):

The Centers for Disease Control says the most important way to prevent the transmission of dangerous diseases is to frequently wash your hands with soap and water and/or use a hand sanitizer. If soap and water are not available it is recommended to use a hand sanitizer that contains at least 60 percent alcohol.[16][17] Alcohol rubs kill many different kinds of bacteria, including antibiotic resistant bacteria and TB bacteria. It also has high viricidal activity against many different kinds of viruses, including enveloped viruses such as the flu virus, the common cold virus, and HIV, though is notably ineffective against the rabies virus.[18] [19] [20] Alcohol rub sanitizers are not very effective against Norovirus (winter vomiting virus) unless they are combined with benzalkonium chloride in a hand sanitizer.[21] Alcohol rubs also kill fungi.[22] University of Virginia Medical School researchers concluded that hand sanitizing is more effective against fighting the common cold than hand washing.[23] Alcohol kills both pathogenic (disease causing) microorganisms as well as resident bacterial flora, which generally do not cause illness. [24] Research shows that alcohol hand sanitizers do not pose any risk by eliminating "good" germs that are naturally present on the skin. The body quickly replenishes the good germs on the hands, often moving them in from just up the arms where there are fewer harmful germs.[25] Alcohol also strips the skin of the outer layer of oil, which may have negative effects on barrier function of the skin. However, washing with detergents, such as commonly used hand soaps, results in a greater barrier disruption of skin compared to alcohol solutions, suggesting a increased loss of skin lipids.[26] [27]

Fortunately, not everyone missed the CDC angle.

Silence

I am about to be travelling for a bit so the blog might be lightly updated until May 2nd.

In the meantime, I strongly recommend trying a few other good sites:

http://www.stat.columbia.edu/~cook/movabletype/mlm/

http://worthwhile.typepad.com/worthwhile_canadian_initi/

http://marginalrevolution.com/

as these are all blogs with good runs of posts. Not on my blog-roll, but also worth noting is Matt Yglesias who has also been putting out some very goos stuff lately.

When people are willing to pay extra not to use your enhancement...

... you may have a problem.

Via Gizmodo by way of Salmon, here's a place that sells glasses that allow you to watch 3D in glorious 2D. If they can just do something about the murky color they'll be onto something.

For more on the failings of 3D, check here.