A Game Theorist’s Approach to Social Distancing
We are often conflicted as to how close we want to be with others. For example, during this pandemic, we know that we should abide by social distancing regulations, yet we crave social interactions. However, despite how much we yearn for human connections, we know from past experiences that the closer we get to others, the more likely tensions will arise and feelings will get hurt.
This dilemma is reflected in the 19th century German philosopher Arthur Schopenhauer’s “hedgehog dilemma.” In this scenario, a group of hedgehogs are trying to keep warm on a cold winter evening. They inch closer to each other in order to warm up, but then their spikes poke into each other. They are forced to move apart, but then they are cold again. Regarding this dilemma, Schopenhauer concluded that there was no solution. You simply cannot have both.
Professor Alvaro Sandroni at Northwestern University reapproached this problem from the game theorist’s perspective. He sets up a two-player game, and he assumes that each player has a preferred distance that they want to keep from the other. The players must choose where they want to stand along a straight line at the same time. The players know the other’s preference, so they can use this knowledge to select their own optimal position.
In Sandroni’s game, he found that two types solutions existed, one pure and one mixed. Sandroni found a pure strategy solution to this problem when both players happen to prefer being the exact same distance apart. However, when one person wants to be closer than the other, there is no pure strategy because there is always a better distance that one player could have selected.
To find a Nash equilibrium in this scenario, you must randomize. As we learned in class, you want to be unpredictable so that the other player does not know what your move will be. Let’s consider an example: Player 1 wants to maintain 6 feet separation from player 2, but player 2 wants to violate social distancing and only stay 3 feet apart from player 1. Sandroni solves that the optimal strategy for player 1 would be to randomly choose between 6 feet to the right and 6 feet to the left of where player 1 thinks that player 2 will be, while the optimal strategy for player 2 would be to stand halfway between these two spots. In the end, player 1 is always happier than player 2, but this is the best that player 2 can do. Any other position may result in greater unhappiness in player 2 because player 1’s choice in position is unpredictable. The fact that player 1 is happier in the end is a result of “oppression by randomization,” as Sandroni writes. The player who wants to be closer is ultimately going to be disappointed because the final distance will always be in favor of the player who wants to keep a greater distance.
Sandroni did not solve the original dilemma presented by Schopenhauer, but his research offers perspective to how we can approach a related problem in which two people’s happiness are at odds with each other. Although you cannot truly randomize your position in real life, Sandroni’s findings teach us that we need to be unpredictable if we want to keep distance from someone who wants to be closer. In the case of maintaining social distance, this could translate to pacing and wiggling around so that the social distancing violators cannot predict your next location. In the case of human intimacy, this could translate to not letting your friends know where you are so that you can maintain your happy distance from them.
Reference: https://insight.kellogg.northwestern.edu/article/social-distance-closeness-game-theory