ECO hw Help

17 Jun ECO hw Help

QUESTION 1

1. The expected payoff of player 1 from the mixed strategy is the __________ of the expected payoff for each of her _________strategies, where the weights are the probabilities given by _____.

A.

product; pure;

B.

weighted average; dominant; player 2

C.

weighted sum; pure;

D.

weighted difference; mixed; nature

15 points

QUESTION 2

1. Consider a two-person game, where player 1 has two strategies and player 2 has three strategies. Which of the following express a mixed strategy equilibrium? [mark all that apply]

A.

where is the probability distribution of player 1 over her pure strategies, similar for .

B.

[(1,0,0), (1,1/2)]

C.

[(p, 1-p,0), (q, 1-q)] and p and q are in the interval [0,1]

D.

[S1, S2] where S1 and S2 are the sets of pure strategies of player 1 and 2.

E.

[(p1, p2,1-p1-p2), (1, 0)] and p1 and p2 are in the interval [0,1]

15 points

QUESTION 3

1. Whenever we add uncertainty to a game and a player would like to outguess the others, ________ a NE in _________ strategies. Players would assign ________ to the its strategies in Si, and this gives us the notion of ___________ strategies.

A.

There is not; mixed; values; dominated

B.

There is; weak; maximin values; maximin

C.

There is not; pure; weights; dominant

D.

There is ; pure ;probabilities; mixed

10 points

QUESTION 4

1. Mark the correct sequence for the following statements:

I. Finite games have at least one Nash equilibrium in pure strategies.

II. A pure strategy may be strictly dominated by a mixed strategy, even if this pure strategy is not strictly dominated by any other pure strategy.

III. A pure strategy can be a best response for a mixed strategy if and only if such pure strategy is also best response to any other pure strategy.

A.

TTF

B.

FFF

C.

TFT

D.

FTF

20 points

QUESTION 5

1. Consider a kicker (K) and a goalie (G) in a soccer game. Suppose that if K kicks to the right and G jumps to the right, the probability of a goal is 0.3. If K kicks to the right and G jumps to the left, the probability of a goal is 0.9. If K kicks to the left, the probability of a goal is 0.8 if G jumps to the right and 0.5 if G jumps to the left. Fill the following matrix with the given probabilities. Assume the kicker is the row player and the goalie is the column player.

L

R

L

,

,

R

,

,

20 points

QUESTION 6

1. What is correct about Nash equilibrium in mixed strategies:

A.

In a two-player game, mixed strategies are a Nash equilibrium if each player’s mixed strategy is a best response to the other player s mixed strategy, and none will unilaterally deviate.

B.

It only exists when all players randomize their pure strategies.

C.

Graphically, NE is given by the intersection of the player s best response payoffs

D.

In equilibrium, the mixed strategy of a player must put positive probability on a given pure strategy only if the pure strategy is itself a best response to the mixed strategy of the other player.