AFAICT, in the Highwayman example, if the would-be robber presents his ultimatum as “give me half your silk or I burn it all,” the merchant should burn it all, same as if the robber says “give me 1% of your silk or I burn it all.” But a slightly more sophisticated highwayman might say “this is a dangerous stretch of desert, and there are many dangerous, desperate people in those dunes. I have some influence with most of the groups in the next 20 miles. For x% of your silk, I will make sure you are unmolested for that portion of your travel.” Then the merchant actually has to assign a probabilities to a bunch of events, calculate Shapley values, and roll some dice for his mixed strategy.
AFAICT, in the Highwayman example, if the would-be robber presents his ultimatum as “give me half your silk or I burn it all,” the merchant should burn it all, same as if the robber says “give me 1% of your silk or I burn it all.”
But a slightly more sophisticated highwayman might say “this is a dangerous stretch of desert, and there are many dangerous, desperate people in those dunes. I have some influence with most of the groups in the next 20 miles. For x% of your silk, I will make sure you are unmolested for that portion of your travel.”
Then the merchant actually has to assign a probabilities to a bunch of events, calculate Shapley values, and roll some dice for his mixed strategy.