Apply the method of backwards induction to compute a Nash equilibrium of the following game. (For the node after Player 1 plays L, it assigns probability 1/4 to player 2's node and probability 3/4 to player l's node) 1 R 1/4, 3/4 1 A B B 4 4 10 4 1 10 2.
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- 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 68,91Consider the following 2-person game, Player 2 A C А 3,3 1,1 0,0 1,1 2,2 0,1 0,0 1,0 0,0 Player 1 B C a) What would you recommend to a player who intends to play action? b) What are the Nash equilibria of the game? c) If you were asked to give a prediction as to what two people playing this game would do, what is your prediction? Why?1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities. What are the pure-strategy equilibria of this game? A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.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)Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they exist
- 3:51 9 M 23 The mixed strategy Nash equilibrium of the following * game is Player 2 R. L Player 1 U 2,2 3,1 D 3.-1 0.0 U with 3/4 probability and D with 1/4 probability for player 1; L with1/2 probability and probability for player 2 with 1/2 U with 1/2 probability and D with 1/2 probability for player 1; L with1/4 probability and R with 3/4 probability for player 2 U with 1/4 probability and D with 3/4 probability for player 1; L with1/2 probability and R with 1/2 probability for player 2 O None of the above. U with 1/2 probability and D with 1/2 probability for player 1; L with3/4 probability and R with 1/4 probability for player 2Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, 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? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.Consider the following game Player 2 E N 4, 4 0, 2 Player 1 M 2, 0 2, 2 В 3, 0 1,0 a) Find the the pure-strategy Nash equilibria b) Find a mixed-strategy Nash equilibria in which Player 1 plays all three of their strategies with positive probability.
- Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.How many Nash equilibria does this game have? hand written plzz
