Jordan's Blog - The Christmas Story

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The Christmas Story

Jordan 2017-12-11

On Christmas Eve 1914, all along the Western Front of the Great War, soldiers on both sides of the trenches noticed a sudden absence of artillery bangs – a momentary and spontaneous ceasefire. In Ypres, Belgium, German troops placed candles along the edge of their trenches and fashioned a makeshift Christmas tree, ornamented with buttons, hats, and cigarettes, and went on to sing Christmas carols into the night. British troops across the division responded with Christmas carols of their own, and soon after, troops were exchanging gifts across no-man’s-land. This happened all over the French, German, and British lines, and proved that uncoordinated efforts to overcome non-pareto-optimal Nash equilibria by rejecting one’s own incentives in favor of the meta-incentive are possible, but only on Christmas.

In the iterated Prisoner’s Dilemma, one of the winning strategies is Tit-for-Tat. You can assume that your partner is trustworthy until they betray you, at which point you tat their tit by betraying them back. If it’s common knowledge that you’ll punish their tits, then this also acts to incentivize them not to betray you in the first place.

But suppose you’re a Tit-for-Tatter playing the iterated PD in a big pool with a bunch of people following a couple of different strategies. We call these people Angels and Demons. Angels always cooperate, and demons always defect. Let’s say that you are matched up with a random person in your pool, and your reward for winning against them by a large enough margin in a series of iterations is that more people start to use your strategy. If we mix a pool with mostly demons and a few angels, say 2/3 and 1/3, and do this over and over, the demons would obviously start to take over. The rare times angels would get matched together and win gains would be far exceeded by the number of times they are matched with demons and taken advantage of. But if we were to take half of the demons and turn them into Tit-for-Tatters so that there’s an even 3 way split, then the angels and Tit-for-Tatters would be at an advantage. Since they outnumber the demons, and angels can win gains when matched with Tit-for-Tatters as well as other angels, and since The Tit-for-Tatters also play sufficient defense against the demons so that their strategy doesn’t really spread, the pool will become dominated with angels and Tit-for-Tatters. As we can see, the benefit of Tit-for-Tat is that it opens you up to cooperation, but not in a way that allows you to be taken advantage of by those with no intention to cooperate.

Suppose we coin a new strategy, Aggressive Tit-for-Tat, which says that you should defect once and thereafter use the regular tit-for-tat strategy. This way you have slightly better gains against angels, and you play slightly better defense against devils. If you get matched up with a regular Tit-for-Tatter, well, you end up in an extremely non-pareto-optimal Nash equilibrium over the course of the iterations, as they continue to punish you for the last time you defected by defecting, and you continue to punish them for the last time they defected by defecting. But since you started it, which means you got to betray your partner one time before they started playing defense, you come out with a small gain. The pareto-optimal solution involves both sides collaborating, as they clearly have the ability to do, but since there is no existing culture of trust, neither side has any incentive to stop punishing the other side for defecting. If we fill a pool with angels, demons, and Aggressive-Tit-for-Tatters, all the angels will slowly be outcompeted, and you end up with a pool wherein everyone is defecting over and over, and any cooperation is immediately taken advantage of unless an angel happens to have been lucky enough to be matched up with another angel.

So introduce another new strategy called Generous Tit-for-Tat. This strategy says that you should use regular tit-for-tat, but every once in a while you can randomly forgive your partner. This way you collaborate with angels, still play pretty good defense against demons, and you also have the ability to spontaneously escape defect-loops with Aggressive-Tit-for-Tatters. Since collaboration yields the highest gains, if you were to introduce some of these into your pool which has become almost all Aggressive-Tit-for-Tatters and demons, you would do very well, the angels would begin to recover, and the demons would begin to die out.

I once heard a story about an economics professor who wanted to prove a point about rational decision making as a consumer. He would bring a twenty-dollar bill to class and hold an All-pay auction to see who gets the money, starting at $1 and going up in $1 increments. In an All-pay auction, bidding is spending, so if you bid one dollar and someone else bids two, you’re out $1 and they get the prize for $2. Predictably, the class would start with low bids – who wouldn’t want a twenty-dollar bill for the low price of $1? – and would often escalate past the point of $20, perhaps between two bidders who don’t want all the money they already spent to go to waste. Once, the professor recounts, the price of the twenty-dollar bill went all the way up to $204 dollars. Supposing the professor went on to selfishly pocket the money (rather than give it to charity, which he does) we would probably agree that on the whole we should be able to do better. Though every individual is incentivized to try and win the twenty-dollar bill for as little money as possible, there might also be a collective meta-incentive to deny a professor trying to make a point the satisfaction of being right. Just as you might choose to adopt the Generous Tit-for-Tat strategy yourself if you were to find yourself in one of the above pools, in hopes that it would lead to a healthier and more trust-infused pool for everyone, you might start this auction by bidding $1, and then $2, and $3, $4, $5, $6 (a total of $21) and then stopping, effectively making a gambit to purchase a collective win for $1, and hoping that your classmates have enough meta-reasoning and meta-incentive to not bid $7.

But generally gambits like this don’t work in real life. Not always because people don’t do the meta-reasoning, but because our meta-incentives are not quite so aligned. We are motivated by social status, politics, and on the whole tend to have different values. Maybe you don’t care about the overall health in the pool as long as you can defect enough to feed your immediate family. Maybe you realize that you can win social status points by messing with the nerd who proposes a $1 gambit in his blog by bidding $7 anyway.

WWI, as it turns out, came with a mostly-aligned incentive of live-and-let-live. Soldiers in the trenches felt this at a deep level, and so when the other side began running across no-man’s-land, our side didn’t decide to immediately resume shooting and end the ceasefire by defecting. But by Christmas the year after, orders had come down that no fraternizing with the enemy was allowed. This at least, allowed for more consistency, and made slightly more sense than the idea that we might spontaneously hop to a peaceful equilibrium on Christmas, only to go back to war right after New Year’s. Real war has a lot to do with politics and you need to consider more than which iterated PD strategy is your favorite. War is complicated. But at the meta level, everyone still prefers peace. Even those who go to war tell themselves that they’re doing it to achieve eventual peace. It just happens that it’s hard to step from our particular equilibrium of continuous war into an equilibrium of continuous peace. It’s hard to step from having 4000 stockpiled nuclear warheads (enough to destroy the world 40 times in a row) and a defense budget of $800,000,000,000 to, let’s say half of that, especially if we have no reason to trust that our enemies are also going to reduce spending on their weapons.

But Christmas is the best holiday because it allows us to do things like exactly that. All the messaging and advertising reminds us that this is the season to think of others (by buying them Hallmark cards and Coca Cola, but think of them nonetheless). Christmas is our culture’s winter solstice celebration, when we huddle together on the coldest and darkest day of the year and say “fuck you nature” by putting up lights and singing songs. It’s the time that we celebrate our ability to trust each other and be close, because all our crops are dead and it’s all we can do to ask our neighbors for theirs. And because our culture has a Christmas, we are able to do things like temporarily create a culture of trust where soldiers on either side can expect the enemy to honor a ceasefire. We are allowed to temporarily forgive and be generous, and we are allowed to be rewarded with gains for that cooperation. Even when the pool is dominated by Aggressive-Tit-for-Tatters and demons, we are allowed to chose Generous-Tit-for-Tat, and wordlessly cooperate with our brothers and sisters who have seen the same light as us – that there is a better world than the one we live in, and it’s only one collective step away.

Even in times of peace there is poverty and disease. Even if you believe war is necessary to arrive at a greater good, there is starvation and disaster. If one Christmas, decades from now, everyone in the world donates 10% of their income to help others, then just the first year’s $7,000,000,000,000 would be enough to solve global poverty, eliminate all treatable diseases, fund research into the untreatable ones for approximately the next forever, educate anybody who needs educating, feed anybody who needs feeding, fund an unparalleled renaissance in the arts, and permanently save every rainforest in the world, with money to spare. (Now imagine if we auctioned that money $20 at a time to business school students!) I am the first to admit the insane extent to which our Christmas traditions are just ways to make us buy things we don’t need and turn the spirit of giving into a commodity. But here’s a more thoughtful and less cynical narrative: Christmas is a fluke in the brokenness of the world, a crack in the system’s armor that lets us do good and trust that others will too, and every year we get one more chance for a small window of time to use our ability to forgive and be generous without fear of being taken advantage of, and maybe we don’t quite hit the mark this year or next year, but I will be back every year putting up candles along my trench and singing songs, and I’d like it if you joined me.