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“Gifts! Especially, gift certificates!” sneered Ebenezer Scrooge. “A finer piece of humbug the world has never seen. Why, for no charge at all, they will convert my hard-earned cash to a card that can be redeemed at one store only. No doubt the store hopes the recipient will lose it. How generous!”

“But, Uncle Scrooge,” Fred explained patiently, “when I buy my wife a gift card for Havisham’s, her favorite fine clothing shop, I know that she will spend the money there, on something she will truly enjoy, when she would hesitate to indulge herself on a purchase made with money.”

“Are there no thrift shops? No doubt she could be attired comfortably enough for a few shillings at Nickleby’s without making herself a slave to fashion. And what, may I ask, does she get for you?”

“Well, for instance,” said Fred, “last year, Clara gave me a gift certificate for Copperfield’s Jewelers. I purchased this reliable timepiece there, when I might have allowed my punctuality to continue to suffer with my sad old pocket-watch if deciding on my own account.”

“A fine watch, nay, a fine waste indeed!” harrumphed Scrooge. “I do quite well with the old pocket-watch my grandfather gave me, fifty years ago, thank you – I wind it three times a day, and have never been late a minute in my life. Now, I suppose your gifts to one another were of equal value?”

“Yes, of course. Neither of us would wish to be less generous than the other.”

“Forgive an old money-lender his arithmetic,” Scrooge began craftily, “but I wish to ensure I understand this aright. You each gave the other a gift certificate for, I shudder to think it, five pounds?”

“That’s exactly it.”

“Bah, my clerk Cratchit and his large family live quite comfortably on five pounds a month, I am sure! You proceeded to use these certificates on goods which your natural sense of thrift and clear-headedness would have told you were mere frivolity?”

“Well, perhaps…”

“Young sir, my long experience in financial matters tells me exactly what you have here: a money-laundering scheme!”


“Protest if you will; there is no other word for it. The final outcome is no different from that if you had each spent your five pounds on goods for yourselves, goods which you yourself would describe as wanton indulgences. By funneling this same money into gift certificates ‘for each other,’ you believe you have cleansed the money of its sinful use, and cleansed yourselves of the sin of waste, turning it into a so-called generous impulse. You convince yourselves you are all such noble creatures while indulging your most frivolous desires. But old Scrooge knows a bit of laundering when he sees it! A fine humbug!” In making this triumphant proclamation, Scrooge experienced the one hollow sort of pleasure of which his small old heart was capable: pleasure in his own cleverness at unmasking those who pretended to be more generous than he, at revealing them to be just as self-interested as the old miser himself, as he always knew they must be.

Fred responded in measured tones, but to those who knew this most affable of gentlemen, the slight steel in his voice would have made it resound as though he used a tone of thunder. “Those of us who believe that to be truly human, one must be a social creature, are not so poor at arithmetic as you seem to think. Yes, a child can understand your argument that purchasing gift certificates is a senseless ritual. Though a ritual may have an arbitrary aspect, this does not make it senseless. When I buy my wife a gift, it causes me to consider what brings her joy, and to empathize with her pleasure at receiving it, and it causes her to think of me when she uses it. And so it is in reverse. Gift-giving may be a ritual, but it is a ritual that brings us closer together. Of course, enhancing our consideration of those closest to us is only the first step. A truer expression of the Christmas spirit is generosity towards those most in need. Those who love and feel loved, as you do not, poor sir, are more likely to be generous to the poor who share our city. Clara and I always plan our charitable work for the year during the Christmas season.”

“Charity, humbug. Making idle people merry is no virtue.”

“There are many other purposes of charity, Uncle, but at the risk of my immortal soul, I shall debate you on your own coldhearted terms. Your logic concerning gifts appears infallible, but you have made what my dear old professor of economic philosophy would call an implicit assumption, and a most unwarranted one.”

“Eh? What’s this?”

“Why Uncle, you have assumed that each of us makes the best possible spending decisions if left entirely to our own devices, in an entirely anti-social world. As you follow the markets, you know it has been a harder few winters than usual for all of us in London. We are all a bit chary of unnecessary spending.”

“Chary, yes, cautious, of course!” Scrooge interjected. “Cautious as well you should be, and not any less so because of a supposed ‘Christmas spirit.'”

“Caution is a fine thing, Uncle, but should it lead us to consume nothing beyond the bare essentials of life? Is it rational for all to live as you do, spurning all material comforts for an ever-growing pile of gold? I am sure you take no pleasure in the thought of leaving your gold to your unworthy next of kin, so perhaps you intend to be buried with it.”

“Bah, perhaps I do, what of it? De gustibus non est disputandum. By your own description, you are no better than I. You prefer ‘comforts’ – indulgences, I call them – I prefer to keep my gold. Simply spare me your pretense of a generous spirit!”

“For the moment, spiritual worth is not the issue. To the extent that decisions are a matter of taste, who is to say that the decisions Clara or I would make as individuals are superior to the decisions we make as a harmonious unit? That point aside,” Fred continued, cutting off the retort rapidly forming on his uncle’s lips, “here is one that even you will appreciate. My dear Prof. Senyek, who is literally generations ahead of his time, acquainted me with the paradox of thrift.”

“What paradox could there be concerning the virtue of thrift?”

“Well, Uncle, if a virtue is, as the noted Prussian Mr. Kant would have had it, that which makes for a good society if followed as a universal law, then thrift, particularly in these hard times, is no virtue.”

“I beg your pardon? You mean to say thrift is an especial virtue in hard times!”

“No. In hard times, if everyone saves more, our factories are under-utilized, and goods rot away on the shelves of stores. The factories and stores reduce their workforce, precious wages are missed, and the icy hand of thrift grips the city’s purse-strings still tighter.”

For the first time, Scrooge was without an immediate retort. Was it possible that his good-for-nothing nephew was teaching him, Scrooge, about practical matters? “Then,” he continued slowly, “if every household does as you do, and bypasses their natural thrift through your most ingenious scheme of gift-giving and supposed generosity, the downward spiral is halted. Stores fill their shelves in anticipation of a great December rush! Factories are employed above their usual capacity!”

With this, Scrooge sprang up with a most uncharacteristic energy, and reached for his hat and coat. “Wherever are you going, Uncle Scrooge?” asked an astonished Fred.

“My fine, dear, boy, I am a major shareholder in Harrod’s. I must tell them at once to redouble their Christmas display, and make sure their leaflets reach all neighborhoods, from the poor to the great. Most importantly, the leaflets must emphasize the noble virtues of ‘generosity’ and ‘Christmas spirit.’ An eminently valuable humbug! Thank you, dear boy! Merry Christmas!” Concluding with this most unlikely of salutations, Scrooge leapt out the door, and he could be heard repeating “Merry Christmas!” with great enthusiasm to all he encountered as he passed through the streets of the city.

Fred was left standing alone in Scrooge’s office, a bemused half-smile on his face. He reflected that in changing his uncle’s mind, he had done all that was humanly possible. Saving the old man’s hardened soul would truly require supernatural intervention.

I’ve been watching NFL football all my life, and endgame timeout-strategy (being susceptible to analysis by non-football people) has always attracted my attention, but there is one numerical quirk with big potential consequences which I only noticed this season. Consider this scenario:

Late in an NFL game, Team A has the ball and a small lead. Team B has 1 timeout left. Team A, on 1st down, runs it up the middle for no gain. The play ends (to be precise, the 40-second play clock is reset) with 2:43 remaining. What is Team B’s strategy?

The obvious thing is to call the timeout now; when it appears not to matter, I mostly see teams use their timeouts on early downs rather than later downs. But in this case, that would be an enormous mistake! Consider the very likely continuations:

Use timeout now:

2nd down: Play begins 2:43, ends 2:38. Clock ticks down to 2:00. Two-minute warning.

3rd down: Play begins 2:00, ends 1:55. Clock runs to 1:16.

4th down: Punt, snap at 1:16.


Save timeout:

2nd down: Play begins at 2:04, ends 1:59. Two-minute warning.

3rd down: Play begins 1:59, ends 1:54. Team B calls final timeout.

4th down: Punt, snap at 1:54.


Using the timeout early costs almost 40 seconds! It costs almost the full value of a timeout, because it removes all the power of the two-minute warning. I can’t actually cite a game from memory where someone screwed this up, but I don’t think I would have been alert to it until recently. Given that I’ve never heard this mentioned on TV, and given the general propensity of NFL coaches to screw up timeout strategy in more obvious ways, I would expect a high proportion of mistakes when this situation arises.

The bottom line: If the clock resets with roughly 2:41-2:49 remaining, don’t use your timeout now. Wait until after the two-minute mark, to make sure you get proper value from the two-minute warning. Note that in college football there is no two-minute warning, so this whole discussion is moot.

One tiny caveat: The recommended strategy does give Team A a free license to throw the ball on 2nd down, since an incomplete pass won’t matter. They might do so and get a first down, ending the game. But there is no way this possibility cancels out the huge time savings. Team A always has the option to throw it anyway, if they want to take the risk of leaving 40 extra seconds. That is, the waiting strategy is (almost) dominant.



This essay started as a short post responding to an article by Greg Mankiw and grew longer than I expected, so to avoid cluttering the blog I switched formats. As you might guess from the potpourri in the title, the essay is intended to be readable by a broad audience. The portions which discuss the use or misuse of economic theory in the tax debate are, it is my fond hope, of interest to economists and accessible to non-economists, as is Mankiw’s article. I began this last week, so it doesn’t refer directly to this week’s big news of the Great Tax Compromise of 2010, but the ongoing negotiations were a major motivation.

I hope this has been enough of a teaser for you to click here.

Tribal Wars and Travian (which is the more recent version of Tribal Wars) is a browser-based strategy game. Millions of players, I guess that mostly teenagers and college students, play the games. Every player starts with a village, where he can build and upgrade various buildings, like a Clay Pit, Stables, Iron Mine, and even an Academy. The player can also train various types of soldiers that help pillage or conquer other villages (and defend one’s own village when someone else tries to pillage or capture it).
My younger kid started to play this game, and so he pulled us all into it: we all manage our village together and are happy with its progress.
The game’s entry in Wikipedia emphasizes the cooperative nature of this game: to reach the game’s goal, which is building a world wonder, one needs huge amounts of resources, which can be supported only by many players. Therefore it is essential to form large coalitions of players who help each other, or “tribes” in the game’s terminology. So the game “is heavily geared toward cooperative play”.

The entry does not tell us that the game has also a non-cooperative aspect: conquering other players’ villages. My son joined the game in quite a late stage, when there are many abandoned villages. These villages keep progressing, but there is no human player behind them, and so when you pillage them, you do not harm anyone. But since they are managed by a computer and are regularly pillaged, their progress is slower than the progress of villages managed by humans. Therefore, when a player wants to conquer another village, it is more tempting to capture a highly developed village managed by a human than a mediocre village managed by the computer. The only problem is that when you capture a human-managed village, there is a human, usually a teenager or a college student, who stops enjoying the game.

My son, who got a pacifist education, does not dream of harming other players. Others think differently. One day we found to our horror that we are attacked by a player who is 10 times stronger than us. Unbelievably we withstood the attack. We then sent an e-mail to the player, telling him that we do not want to fight, and that the board is large enough so that we can both enjoy the game. The response was a raid.

I then explained to my son the role of a tribe: your tribe should assist you when in need. He was exposed to the game through a friend, and joined the friend’s tribe. The problem was that the friend’s tribe was rather weak, and anyway was based on another corner of the board, so that the other tribe members could not help him. We switched to a closer tribe with strong players, and let the vicious attacker know that we did it, so that he will not attack us once again by mistake. We now prosper and our village progresses faster than ever.

Why do I tell you about this experience? First, I was left open-mouthed with this young fellow, the attacker, who is willing to kick a player from the game, even though the other player asks to be left alone, to enjoy the game. Two thousands years ago (and even few hundreds years ago) life did not count much. It seems that when some people do not see the other person, they may harm him. Some may say that it happens only in Israel, because of the long period in which the country mistreats others, but I suspect that it happens elsewhere as well.

Second, I found the game very useful in explaining to the kids many facts about life and strategic thinking: the importance of information (the attacker failed in his attack because he did not know how many soldiers we had), planning (what is the next building that we should upgrade), the use of information (when the attacker sends soldiers, is it to raid us or to conquer us? can we withstand another attack?), strategic thinking in general (what should we do to survive? what will the attacker do?), and of course, the fact that having strong friends is very useful.

Bottom line: this game is fun but addictive. Stay away from it.

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