Consider the following game in extensive form, involving the chance parameter p. P[T] = p (0,0) n u P[H] = 1-p B h d P[T] = P (-80, 80) (20,-20) (60,-60) t (0,0) n P[H] = 1 (0,0)
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![Consider the following game in extensive form, involving the chance parameter p.
A
P[T] = P
(0,0)
N
U
P[H] = 1-p
h
t
B
h
d
P[T] = P
(-80, 80) (20,-20) (60,-60)
t
(0,0)
n
P[H] = 1-p
(0,0)
Suppose that the strategy profile (u, h) is played and player B receives an expected payoff of 12.
What is the value of p? (Report your answer in decimal form, rounding if necessary to two places.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35bc7cfb-e38c-45d6-8cb2-8c987ddfb016%2F37283ba6-e69e-40b1-b664-b40bfe59e437%2F68yefk4_processed.jpeg&w=3840&q=75)
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- Consider the following game in extensive form, involving the chance parameter p. PT] =P (0,0) N Answer: U P[H] = 1-p h B P[T] = P h d (-60,60) (20,-20) (40,-40) t (0,0) N P[H] = 1-p (0,0) Suppose that p = 0.75 and the strategy profile (u, h) is played. What expected payoff does player B receive? (Report your answer in decimal form, rounding if necessary to two places.Find an equilibrium in the following game, with Nature moving first, with fixed probabilities as shown. (0,2) (2,2) B Q 2 (4,0)N N (6,0) .1 (0,0) (2,0) F .9 F B Q (6,2) N 2 1 -(4,2)Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)
- Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) Defect (2, 12) (4,4) (12, 2)Consider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?Suppose that you graduate from college next year and you have two career options: 1) You will start a job in an investment bank paying a $100,000 annual salary. 2) You will start a Ph.D. in economics and, as a student, you will receive a $20,000 salary. You are bad with decisions, so you are letting a friend of yours decide for you by flipping a coin. The probabilities of options 1 and 2 are, therefore, each 50%. a) Illustrate, using indifference curves, your preferences regarding consumption choices in the two different states of the world. Assume that you are risk-averse. [Include also the 45 degrees line in your figure] b) Now show how the indifference curves would change if you were substantially more risk averse than before. Explain. c) Now show the indifference curves if you are risk neutral and if you are risk loving. d) Show your expected utility preferences from point a) mathematically.
- (ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D(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?Two players play the following game for infinite times. For the player to continue to cooperate what would be the ranges of their discount factor, δ_1 and δ_2, respectively? cooperate betray cooperate (10,20) (-25,30) betray (15, -22) (-12, -18)
- With what probability does player 1 play Down in the mixed strategy Nash equilibrium? (Input your answer as a decimal to the nearest hundredth, for example: 0.14, 0.56, or 0.87). PLAYER 1 Up Down PLAYER 2 Left 97,95 47, 33 Right 8,43 68,91Find the mixed strategy Nash equilibrium by using the concept of probabilities. Player X West{W} East{E} Player Y (0,10) South{S} (7,8) (4,8) (0,12) North{N}Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.
