Question: 5. (20 points) FIGURE 1 (next page) represents a simultaneous-move game between Tara and Jen. If Tara chooses to play Down, then the state of

5. (20 points) FIGURE 1 (next page) represents a simultaneous-move game between Tara and Jen. If Tara chooses to play Down, then the state of the market (Bull or Bear with equal probabilities) affects the relevant payoffs. Jen observes the state of the market but Tara does not. If Tara chooses to play Left, then the state of the market is irrelevant. (a) Is this a constant-sum or variable-sum game? How do you know? (b) Is this a game of complete or incomplete information? Is this a game of perfect or imperfect information? Explain. (C) Write down all strategies available to each player (d) Construct a Bayesian normal form (matrix) representation of this game. (e) Find all Bayesian-Nash equilibria (BNE) in pure strategies. (0,4) Left Jen Tara (4,0) Down (2, 2) (4,0) Bull Bear Jen Nature (0.5) (0.5) (0,0) (0,4) FIGURE 1 - Payoffs are (Tara, Jen) 5. (20 points) FIGURE 1 (next page) represents a simultaneous-move game between Tara and Jen. If Tara chooses to play Down, then the state of the market (Bull or Bear with equal probabilities) affects the relevant payoffs. Jen observes the state of the market but Tara does not. If Tara chooses to play Left, then the state of the market is irrelevant. (a) Is this a constant-sum or variable-sum game? How do you know? (b) Is this a game of complete or incomplete information? Is this a game of perfect or imperfect information? Explain. (C) Write down all strategies available to each player (d) Construct a Bayesian normal form (matrix) representation of this game. (e) Find all Bayesian-Nash equilibria (BNE) in pure strategies. (0,4) Left Jen Tara (4,0) Down (2, 2) (4,0) Bull Bear Jen Nature (0.5) (0.5) (0,0) (0,4) FIGURE 1 - Payoffs are (Tara, Jen)

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