Question

QUESTION 1 It's always irrational to play a strategy that will result in a Pareto-dominated outcome. True or false? True False QUESTION 2 Common Knowledge.* Suppose that Ava and Bai, two friends, are sitting across from each other drinking coffee at a local cafe. Suddenly (and improbably), a gust of wind blows Torero blue hats on to each of their respective heads. Ava is now wearing a Torero blue hat and Bai is now wearing a Torero blue hat. Because they are sitting across from each other, they can see the color of the hat on the other's head. But they cannot see the color of the hat on their own head. (And the hats came from above, so neither of them saw the hats coming.) Everyone else in the cafe (an entirely hat-less bunch, by the way), awed by this unlikely occurrence, are looking at Ava and Bai. The other cafe-goers can all clearly see that now both Ava and Bai are wearing Torero blue hats. Claim: It is common knowledge among everyone in the cafe that at least one person in the cafe is wearing a Torero blue hat. True or False? [Hint: Recall that some fact, p, is common knowledge just in case everyone knows that p, everyone knows that everyone knows that p, everyone knows that everyone knows that everyone knows that p, ... and so on and so forth.] *Warning: This question is tricky! True False QUESTION 3 If strategy D strictly dominates all your other strategies, then, for any strategy the other player might play, strategy D is your best response. True or False? [Hint: Given what all other players are doing, a strategy is a best response just in case a player cannot do better by switching to a different strategy.] True False

QUESTION 1
It's always irrational to play a strategy that will result in a Pareto-dominated outcome.
True or false?
True
False
QUESTION 2
Common Knowledge.*
Suppose that Ava and Bai, two friends, are sitting across from each other drinking coffee at a local cafe. Suddenly (and improbably), a gust of wind blows Torero blue hats on to each of their respective heads.
Ava is now wearing a Torero blue hat and Bai is now wearing a Torero blue hat.
Because they are sitting across from each other, they can see the color of the hat on the other's head. But they cannot see the color of the hat on their own head. (And the hats came from above, so neither of them saw the hats coming.)
Everyone else in the cafe (an entirely hat-less bunch, by the way), awed by this unlikely occurrence, are looking at Ava and Bai. The other cafe-goers can all clearly see that now both Ava and Bai are wearing Torero blue hats.
Claim: It is common knowledge among everyone in the cafe that at least one person in the cafe is wearing a Torero blue hat.
True or False?
[Hint: Recall that some fact, p, is common knowledge just in case everyone knows that p, everyone knows that everyone knows that p, everyone knows that everyone knows that everyone knows that p, ... and so on and so forth.]
*Warning: This question is tricky!
True
False
QUESTION 3
If strategy D strictly dominates all your other strategies, then, for any strategy the other player might play, strategy D is your best response.
True or False?
[Hint: Given what all other players are doing, a strategy is a best response just in case a player cannot do better by switching to a different strategy.]
True
False

Added by Sara S.

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