The strategy profile I describe is where each person has the following strategy (call it “Strategy A”):
If empty history, play 99
If history consists only of 99s from all other people, play 99
If any other player’s history contains a choice which is not 99, play 100
The strategy profile you are describing is the following (call it “Strategy B”):
If empty history, play 99
If history consists only of 99s from all other people, play 99
If any other player’s history contains a choice which is not 99, play 30
I agree Strategy B weakly dominates Strategy A. However, saying “everyone playing Strategy A forms a Nash equilibrium” just means that no player has a profitable deviation assuming everyone else continues to play Strategy A. Strategy B isn’t a profitable deviation—if you switch to Strategy B and everyone else is playing Strategy A, everyone will still just play 99 for all eternity.
The general name for these kinds of strategies is grim trigger.
The strategy profile I describe is where each person has the following strategy (call it “Strategy A”):
If empty history, play 99
If history consists only of 99s from all other people, play 99
If any other player’s history contains a choice which is not 99, play 100
The strategy profile you are describing is the following (call it “Strategy B”):
If empty history, play 99
If history consists only of 99s from all other people, play 99
If any other player’s history contains a choice which is not 99, play 30
I agree Strategy B weakly dominates Strategy A. However, saying “everyone playing Strategy A forms a Nash equilibrium” just means that no player has a profitable deviation assuming everyone else continues to play Strategy A. Strategy B isn’t a profitable deviation—if you switch to Strategy B and everyone else is playing Strategy A, everyone will still just play 99 for all eternity.
The general name for these kinds of strategies is grim trigger.