Wednesday, December 8, 2021
When I was very much younger, in the pre-computer age, I read a science fiction story that had been inspired by game theory, which was a hot topic at the time. as it focused on the strategies for atomic warfare. In the story, Earthlings were engaged in a space war with aliens. Our spaceships had deep-space dogfights with their spaceships. At critical points in every fight, our ships’ tactics were determined by spinning a sort of multisided dreidel and taking the action indicated by the number that came up as the result of the spin. The captain also spun a different dreidel when deciding on a counter-move to each of the alien’s actions. There was a probability-based idea behind this approach based on game theory. Our hope was the game theory ideal: a strategy that would win, on average, against any counter-strategy.
The system worked perfectly, or rather optimally. The Earthlings won most of the battles because, on average, they always inflicted more casualties on the aliens than they suffered in the encounters. The Earthlings were sure that it was only a matter of time before the aliens realized that continued fighting was hopeless and sued for peace. Indeed, it was odd that they had not already done so, since they seemed to be quite as intelligent as the Earthlings were and certainly knew that they were losing.
Then one day the Earthlings captured an alien ship intact instead of blowing it up. In many respects, the layout of the alien ship was surprisingly similar to that of an Earth ship. When they examined the strategy room, the Earthlings discovered that the aliens were also using a probability dreidel to dictate tactics. But the alien dreidel had different numbers that dictated different tactics.
When the Earthlings did the math, they found that the aliens’ dreidel was causing the aliens to lose almost every battle. For example, in response to the Earthlings’ tactics, the alien dreidel always dictated maneuvers that cost them more casualties than their Earthling enemies. The Earthlings congratulated themselves on their superior mastery of game theory and probability. This was why they were winning. But the discovery created a puzzle. The aliens did not seem stupid. How had they made such a fundamental error?
Upon looking still deeper, one of the analysts discovered the answer. Although each move dictated by the alien dreidel led to the loss of more alien lives than Earthling lives, it also resulted in the destruction of a greater number of Earth ships than the number that was lost by the aliens. It turned out that the aliens believed that they were winning every engagement based on spaceship casualties and the Earthlings believed that they were winning every engagement based on human/alien casualties.
By its own lights, each side was winning the war. And it would go on forever.
At the time I thought that this story was profound, and I still do. But I now realize that its charm would be lost on an economist. Differences in personal valuation such as those between the Earthlings and aliens are the engines that drive our economy. Differences in personal valuation are essential to all exchange transactions in which each side receives something that it values more than it values what it gives up.
Of course, in a war the objective is not so much the enhancement of one’s own utility as it is the destruction of the enemy’s utility. I cannot remember whether the story pre-dated the Vietnam War, but if it did, it was eerily prescient. America’s military believed that it was winning based on what it cared about (body counts) right up until the time when it discovered that it was losing based on what the North Vietnamese cared about (endurance). Our later wars have exhibited similar asymmetries.
The story may also have some relevance to the current economic competition between capitalist and non-capitalist countries. If the former are in it solely for short-term shareholder returns and the latter are in it for long-term growth and stability, conditions may lead each side to believe that it is winning. For a while. If precedent holds true, when one side finally triumphs, we may expect the loser to continue to argue that it was really the winner.
And on a more mundane note, we can see the parable’s relevance to any institution, such as a law school, in which institutional goals are disputed. Whether an institution is succeeding or failing is entirely a matter of preference, of what goals are imputed to the institution by the person making the judgment. Many institutions see themselves as succeeding even though their performance would be rated a failure by other institutions with different values and aspirations.
Indeed, it is quite possible that each of two law schools may see itself as succeeding and the other as failing, one because it is counting diversity and equity and the other because it is counting prestige and research. Just like the Earthlings and aliens.
[i] This is true. I’m not passing this off as my own. I would cite to the story but I was unable to find it on the internet. If the reader knows where I got it, I will happily amend this post and cite the original source.