Slow down until I am just ahead of the front bandit and say,
"As you know, I am a perfect shot (because I'm a hero) and I could kill you right now. But if you stop chasing me and run the other direction, I won't kill you, and maybe I'll kill the next guy instead." On the off chance he doesn't take this deal, I kill him and offer the deal to the next guy, who will definitely take the deal, as will the other 38 bandits.
There might be some clever game-theoretic method the bandits could use to avoid this, but these are bandits, not perfectly rational game theorists, so they won't figure it out.
Cutting the cord to the Doomsday machine is something that the UK might actually do. Publicly the UK states it will always retaliate in case of a nuclear war. But whenever the Prime Minister is elected he/she writes a hand written letter to the nuclear submarines on what to do in case of a nuclear attack. The options are: Retaliate, Do Not Retaliate, Use best judgment, or follow the United State’s orders. This letter is sealed and never read and is only to be opened when the nukes fly. When the Prime Minister leaves office the letter is burned. So it’s entirely possible that every Prime Minister “cuts the cord” so to speak. (https://en.m.wikipedia.org/wiki/Letters_of_last_resort)
Re "Two guys in a bar get in an argument ": Didn't somebody write a song about that? The chorus ended with "You don't mess around with Friedman" or suchlike.
Re the Equimarginal Principle: I was going through customs in the Mumbai airport. After a while standing in the line that was closest to me, I noticed that the line to the left was running faster. There were two customs agents serving the same line! So ceteris non-paribus, I should have gotten on the longest line, as other people noticed the same thing.
The solution I thought of for the first puzzle:
Slow down until I am just ahead of the front bandit and say,
"As you know, I am a perfect shot (because I'm a hero) and I could kill you right now. But if you stop chasing me and run the other direction, I won't kill you, and maybe I'll kill the next guy instead." On the off chance he doesn't take this deal, I kill him and offer the deal to the next guy, who will definitely take the deal, as will the other 38 bandits.
There might be some clever game-theoretic method the bandits could use to avoid this, but these are bandits, not perfectly rational game theorists, so they won't figure it out.
Cutting the cord to the Doomsday machine is something that the UK might actually do. Publicly the UK states it will always retaliate in case of a nuclear war. But whenever the Prime Minister is elected he/she writes a hand written letter to the nuclear submarines on what to do in case of a nuclear attack. The options are: Retaliate, Do Not Retaliate, Use best judgment, or follow the United State’s orders. This letter is sealed and never read and is only to be opened when the nukes fly. When the Prime Minister leaves office the letter is burned. So it’s entirely possible that every Prime Minister “cuts the cord” so to speak. (https://en.m.wikipedia.org/wiki/Letters_of_last_resort)
Re "Two guys in a bar get in an argument ": Didn't somebody write a song about that? The chorus ended with "You don't mess around with Friedman" or suchlike.
Re the Equimarginal Principle: I was going through customs in the Mumbai airport. After a while standing in the line that was closest to me, I noticed that the line to the left was running faster. There were two customs agents serving the same line! So ceteris non-paribus, I should have gotten on the longest line, as other people noticed the same thing.