. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects 22, with payoff functions ₁ and 7₂. Find the best response for P2, as the function 2₂ = BR₂(x₁), for each given #₂: (a) (b) (c) T₂(x1, x2) = (1400 – x1 − x2)x2 – 13.x²2 T₂(x1, x2) = T₂(X₁, X₂) = 100x2 + 3x1x2 − 14x₁ −30x1x² 15x2 x² + x² +1

(b)  Assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game?

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Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).

In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.

Consider the following game: p 2,10 0,5 5,2 0,5 5,10 Which of the following is FALSE for the SPE of this game? a. If p in [0.6, 1], then playing x is an equilibrim strategy for player 1 b. If p in [0, 0.6], then playing y is an equilibrim strategy for player 1 C. For all possible p values in [0,1], playing x is an equilibrium strategy for player 1 y y R Nature 1 2 1-p y R X 2,10