> This statement is demonstrably false. Yes, people intuitively apply game theory all the time. People do intuitively apply game theory, but they do so in ways that aren't strictly rational.
Rationally, deterrence is a function of the penalty adjusted by the odds of being caught and convicted. which means that doubling the penalty should have the same additional deterring effect as doubling the odds of conviction. However, increasing penalties has a relatively small deterring effect, and increasing enforcement a relatively large one.
One way to explain this is to assume that getting caught and convicted has large fixed costs that are independent of the length of sentence.
This tends to cut against the dominant tough-on-crime narrative that focuses on increasing penalties, BTW, but for some reason hiring more judges, prosecutors, public defenders, detectives, CSIs and other people to solve cases and actually go to trial isn't as popular as just mandating longer sentences (and coercing defendants to agree to a plea deal).