Behavioral eco lect 6: Strategic interaction part 3
First-order iterated dominance
Elimination of first-order dominated strategies:
Choosing a number larger than 100p is first-order dominated: • the mean number can be at most 100
→ the target number can be at most 100p
→ choosing x > 100p is always worse than choosing 100p.
Second-order iterated dominance
Elimination of second-order dominated strategies:
Choosing a number larger than 100p^2 is second-order dominated:
If you believe that others do not use first-order dominated strategies,
you believe that nobody will choose a number above 100p.
→ p times the mean can be at most 100p^2
→ choosing x>100p^2 is always worse than choosing 100p^2
→ the mean can be at most 100p
Third-order iterated dominance
nth-order iterated dominance
Elimination of third-order dominated strategies:
Choosing a number larger than 100p^3 is third-order dominated: If you believe that others do not use second-order dominated
strategies, you believe that nobody will choose a number above 100p^2.
→ p times the mean can be at most 100p^3
→ choosing x>100p^3 is always worse than choosing 100p^3
→ the mean can be at most 100p^2
nth order iterated dominance is defined similarly.
Letting n go to infinity leads to the Nash equilibrium.
Guessing game in practice SLIDE 26/57
Does it show that one’s utility may depend on more than one’s own
payoff?
→ no, even if you want payoffs to be distributed fairly, it is very unlikely that you would prefer not to win this game.
Two possible reasons left:
Why don’t people play the Nash equilibrium?
(1) Either you have limited strategic reasoning, or
(2) You believe that others have limited strategic reasoning
Level-k players
Level-0 players: randomly pick a number between 0 and 100
Level-1 players: believe that all others are level-0 players → mean will
be 50 → play 50p
Level-2 players: believe that all others are level-1 players → mean will be 50p → play 50p^2