Algorithms are a staple of modern life. People rely on algorithmic recommendations to wade through deep catalogs and find the best movies, routes, information, products, people and investments.

The original version of this story appeared in Quanta Magazine. Imagine a town with two widget merchants. Customers prefer cheaper widgets, so the merchants must compete to set the lowest price.

Deepfakes – essentially putting words in someone else’s mouth in a very believable way – are becoming more sophisticated by the day and increasingly hard to spot. Recent examples of deepfakes include ...