Consider a game where player 1 must choose T or M or B, player 2 must choose L or R, and their utility payoffs (u1, u2) depend on their choices as follows: Player 1 \ Player 2 L R T 9, 3 0, 0 M 4, 3 6, 5 B 8, 9 1, 2 (a) Show a randomized strategy that strictly dominates B for player 1.
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- In the following symmetric general sum game (2, 2) (0,0) (0,0) (0,0) (0,0) (2, 2) (0,0) (2,2) (0,0) (i) Find all pure Nash equilibria. (ii) Find all mixed Nash equilibria in which all probabilities are positive. (vi) Which of these are evolutionary stable strategies?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 68,914. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.
- 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.W X Y Z 47, 15| 39, 41 45, 53 12, 56 In equilibrium, what is the probability that player 1 will use the pure strategy X in this game?F G H 1 3 6 3 A 6. 8. 8 5 3 B 3 3 4 4. 9. C 5 3 a.) Find all pure-strategy Nash equilibria of the above game. b.) * Prove that there is a Nash equilibrium in which Player 2 chooses H, while Player 1 chooses A with probability 0.4 and chooses C with probability 0.6. 00 2,
- 9 00 3 -2 -8 A = ( ) and B = 03 -5 -2 Let I be the bimatrix game whose payoffs are described by A for the row-player and B for the column- player. 1. Compute all mixed Nash equilibria of T. 9asap8) Find the mixed strategy Nash equilibrium of the following normal form game. Player 2 T1 T2 T3 2, 3 3, 5 1, 1 Player 1 S2 1, 4 4, 3 0, 5 Player 1 attaches probability (S1, S2) = () and Player 2 attaches probability (T1, T2, T3) = ( ) Player 1 attaches probability (S1, S2) = (.) and Player 2 attaches probability (T1, T2, T3) = (qi, 42, 1 – q1 – 92) where q1 , and 0 < q2 S %3D Player 1 attaches probability (S1, S2) = (G,;) and Player 2 attaches probability (T1, T2, T1) = (qı.42, 1 – q1 – 42) where 0 < qi <, and q2 = 3. Player 1 attaches probability (S1, S) = (;, -) and player 2 attaches probability (T1, T2, T3) = (1.42, 1- q1- 42) where 0 s qı s and q2 =
- 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.Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.Consider a game in which two players simultaneously pick an integer from 1 through 10. Let s1 denote choice of player 1, and let S2 denote the choice of player 2. If s1 7 82 then player 1's payoff is: Si + 82 2 and player 2's payoff is 10 – ,*. Si + 82 2 If s1 = 82 then each player gets 5. How many pure strategy Nash equilibria does the game have (you will get full points if you are within 2 of the correct answer)? Numerical answer