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Economics Homework

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:
  2. Finite games have at least one Nash equilibrium in pure strategies.
  3. 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.
 LR
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.

 

 

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