1\2 X Y Z A 8,6 12,5 5,2 B 4,8 8,10 10,12 Suppose Player 2 believes Player 1 will pay a mixed strategy θ1 (A,B) = (θ, 1- θ). Find a range of the frequency of play of A (i.e., values of θ) that makes the pure strategy Y a best response. The minimum value of θ = _____ The maximum value of θ = _____

Three firms share a market. The demand function is P(q1, 92, 93) = 10 – q1 – 92 – 93, where q; is the output of firm i, Player i. The marginal cost per unit for each firm is zero. Suppose firm 1 is a market leader, and that firm 2, and firm 3 choose q2 and q3 simultaneously after observing q1 Find the SPE of this game. How much is produced by firm 2? Numerical answer How much is produced by firm 1, 2, and 3?

Consider the following game   1\2 Y Z A 10,3 3,9 B 8,5 6,1   Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____

1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1

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If a strategy profile is a Nash equilibrium, there is at least one player that could achieve higher payoffs by deviating.(a) True. (b) False.

Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)?      Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)

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Channels 7 and 10 are the only television networks. They want to capture as much of the market as possible because it helps them earn more advertising revenue. Each channel can choose to show a cooking or a reality show on Sunday night. If they both airing cooking shows or both airing reality shows, Channel 10 gets 60% of the market. If Channel 10 is showing a cooking show and Channel 7 is showing a reality show, Channel 10 gets 70% of the market. If Channel 10 is showing a reality show and Channel 7 is showing a cooking show, Channel 7 gets 45% of the market. In a sequential game, Channel 7 moves first. What is true? Group of answer choices Channel 7 will choose reality. Channel 7 has a second mover advantage. Channel 10 will choose cooking. Channel 10 will choose reality. Channel 7 will choose cooking.