Dominant strategies
Econ 171
Clicker Question
Player 2
Strategy A
Strategy A
Player 1
Strategy B
1,3
5, 3
2, 4
7, 2
Strategy B
A ) Strategy A strictly dominates Strategy B for both Players.
B) Strategy B strictly dominates A for Player 1. Strategy A weakly dominates B for Player 2.
C) Strategy B strictly dominates A for Player 1. Strategy A strictly dominates B for Player 2.
D) Strategy B strictly dominates Strategy A for both players.
E) No strategy in this game is strictly dominated
Strict and Weak Dominance
• Strategy A strictly dominates strategy B for a
player if that player gets a higher payoff from
doing A than from doing B no matter what
the other player(s) do.
• Strategy A weakly dominates strategy B for a
player gives at least as high a payoff no
matter what the other player(s) do and for
some actions of the others gives a higher
payoff.
Game Theory Doctrine (A tautology)
• A rational player who understands the payoffs
of a game and who tries to maximize his own
payoff will
A) never use a strictly dominated strategy.
B) will always use a strictly dominant strategy if
one exists.
Dominant strategies?
Player 2
Strategy A
Player 1
Strategy A
Strategy B
Strategy B
1 0 , 10
0, 11
1 1, 0
1, 1
Does either strategy strictly dominate the other for
Player 1?
Does either strategy strictly dominate the other for
Player 2?
What is the predicted outcome?
What are games like this called?
How about this one?
Player 2
Strategy A
Player 1
Strategy B
Strategy A
1 0 , 10
0, 10
Strategy B
1 0, 0
1, 1
Does either strategy strictly dominate the other
for Player 1?
Does either strategy weakly dominate the other
for Player 1?
How about player 2?
How would you play? Why?
Rousseau’s Stag Hunt
Player 2
Stag
Stag
Player 1
Hare
2 , 2
1, 0
Hare
0, 1
1 , 1
Are any strategies weakly dominated?
Are any strategies strictly dominated?
How would you play?
Gaming Pigs
(Iterated dominance)
Are there dominated strategies for Big Pig?
How about Little Pig?
How would you “solve” this game?
What went on in the pigpen
Kidnapping with imperfect information
Strategic Form
Kidnapping with Perfect Information
Kidnapping with complete information
Vivica
Guy
Pay Ransom
Don’t Pay Ransom
Kidnap-- Kill if R, Kill if NR
4,1
2,2
Kidnap—Release if R, Kill if NR
5,3
2,2
Kidnap— Kill if R, Release if NR
4,1
1,4
Kidnap—Release if R, Release if NR
5,3
1,4
Don’t Kidnap– Kill, Kill
3,5
3,5
Don’t Kidnap—Release, Kill
3,5
3,5
Don’t kidnap--Kill, Release
3,5
3,5
Don’t kidnap—Release, release
3,5
3,5
Are any strategies dominated for either player?
Clicker Question
A) No strategies are strictly dominated for Player 1. Strategy w is
dominated for Player 2
B) No strategies are strictly dominated for either player.
C) Strategy c is strictly dominated for Player 1. Strategies w and x
are strictly dominated for Player 2.
D) Strategy d is strictly dominated for Player 1. Strategies x and y are
Strictly dominated for Player 2.
E) No strategies are strictly dominated for Player 1. Strategies x and y are
Strictly dominated for Player 2.
Iterated elimination and Common Knowledge
Strategy a dominates c for Player 1. Strategy y dominates w and x for
Player 2. Rational players won’t use these strategies. If each knows other
is rational, then Player 2 know s that 1 won’t play c and 1 knows that 2
won’t play w or x.
If both are rational and believe other is rational,
Player 1 knows that 2 won’t play x or y, so Player 1 can eliminate b.
Player 2 knows that Player 1 won’t play c, so Player 2 can eliminate y.
If Player 1 knows that Player 2 knows that Player 1 is rational, then
Player 1 knows Player 2 will Play z. What will Player 1 do?
Does Player 1 have a dominated strategy?
Hint: Compare b and d.
Does Player 2 have a dominated strategy?
Hint: Compare y and z.
If each knows the other won’t play a
dominated strategy, we have a
smaller game.
Reduced Game after one iteration.
This is the game if each knows that the other is rational
and each knows that the other knows that the other is rational.
Are there any dominated strategies?
Reduced Game after 2 rounds of iterated elimination of
strictly dominated strategies.
Reduced Game after 3 rounds of iterated elimination.
Are there any strictly dominated strategies in this game?
We have eliminated 12 of 16 strategies, but to get any further,
We’re going to need more tools.