By Eugenia Cheng
June 28, 2024
When I submit a draft piece of writing—a book, a research paper or even this column—I often assume the worst and convince myself it will be rejected. I do much the same while awaiting medical tests. This might sound like rational preparation for potentially disappointing news, but I‘ve realized that expecting the worst result doesn’t help me deal with it, the few times it has occurred. I decided to turn to game theory instead to help me strategize.
iStock image
Game theory is a branch of mathematics that expresses decision-based scenarios in a game-like format, which allows mathematical techniques to be used to study strategies and outcomes. The usual setup is that there are a number of players, each of whom has a fixed set of possible moves, and each combination of moves from different players produces a predetermined outcome. The outcome might just be win, lose or draw, as in a simple game like tic-tac-toe. It might be a numerical payoff, as in a gambling or investment-type situation. Or it might be a notional payoff, so that good and bad outcomes can be quantified rather than being black and white.
Basic games involve just two participants, each of whom has the same two possible moves. The game of “chicken” is one such game, in which two people are approaching each other head on and will collide if nobody moves out of the way. Each player then has two choices: swerve or keep going straight ahead. It might seem rational to always swerve to avoid the collision, but game theory demonstrates that there is no clear-cut best (or “dominant”) strategy that maximizes results in both cases, because if your opponent swerves, you have swerved for no reason.
In the case of my mental preparation, it’s a simpler situation because there’s really only one player—me. (I can treat “fate” as my opponent, though fate is not deliberately trying to maximize its own payoff.) We can call this one-player version “decision theory” rather than game theory. I can still analyze the situation in the same way, considering each of fate’s possible “moves.”
If the news is good, then expecting the worst is actually harmful, because it means I spent some time feeling bad unnecessarily. If the news is bad, then expecting the worst still doesn’t help. It just means I feel bad in advance of really needing to. So in both scenarios, not expecting the worst was a better strategy for me; that means it’s a dominant strategy. The same applies to any time I am hoping for one type of news over another, such as when I’ve applied for a job or been shortlisted for a prize.
The field of game theory takes the math much further. One form of analysis puts different moves into a mathematical structure where the effect of incrementally adjusting the payoffs can be measured. Another can be used to prove under what circumstances dominant strategies exist. The mathematician John Nash was awarded a Nobel Prize in economics for finding something that came to be called a Nash equilibrium: a combination of moves after which no different choice could improve anyone’s results.
There are also wide applications beyond economics: for instance, analyzing arms races or the notion of nations cooperating to address climate change. Disagreement remains among mathematicians about whether game theory is merely descriptive or can also be prescriptive, telling people how to make better decisions. Personally, I am trying to use it prescriptively but with limited success, given that I’m still nervous about submitting this column. If you are reading it, then I imagined the worst needlessly.
Dow Jones & Company, Inc.
