Dominant strategies

Econ 171

Clicker Question

1 , 3 5, 3

2, 4 7, 2

Player 2Strategy A Strategy B

Player 1

Strategy A

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?

1 0 , 10 0, 11

1 1, 0 1, 1

Strategy A

Strategy A Strategy B

Strategy B

Player 1

Player 2

Does either strategy strictly dominate the other forPlayer 1? Does either strategy strictly dominate the other forPlayer 2? What is the predicted outcome? What are games like this called?

How about this one?

1 0 , 10 0, 10

1 0, 0 1, 1

Strategy AStrategy A Strategy B

Strategy BPlayer 1

Player 2

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

2 , 2 0 , 1 1 , 0 1 , 1

StagStag Hare

HarePlayer 1

Player 2

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

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

Vivica

Guy

Are any strategies dominated for either player?

Clicker Question

A) No strategies are strictly dominated for Player 1. Strategy w is dominated for Player 2B) 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, thenPlayer 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.